1 February - An unprecedented rush for Telstra shares helps vault Australian share prices to a record high, as investors focus on the continued strong performance of the local economy. The all ordinaries index surges 29.9 points. 
3 February - An industry review into Queensland's diving industry is released and prompts the Queensland Government to announce its plans to impose jail time or hefty fines on operators falling short of safety requirements. 
19 March - John Brumby resigns as leader of the Victorian Labor Party.
21 March - Channel Nine's 60 Minutes programme airs a controversial report which claims that former Prime Minister Paul Keating lied to Parliament about when he divested himself of his joint share in a Darling Downs piggery, as well as accusing him of fleecing his business partner Al Constantinidis of the majority of the profits.
22 March -
Victorian Shadow Treasurer Steve Bracks becomes leader of the Victorian Labor Party.
Tropical Cyclone Vance hits the West Australian coast with winds of 230km/h. The small coastal town of Exmouth is badly damaged.
Dick Smith (entrepreneur) chairman of the Civil Aviation Authority resigns, followed by board member Janine Shepherd the following day.
23 March - Prime Minister John Howard is criticized by the Opposition and Democrats for his proposal that the concept of "mateship" be introduced into a preamble to the Australian Constitution. He also creates controversy by proposing that Aborigines should be referred to in the preamble as having "inhabited" the land rather than being "custodians" of it.
24 March - Media mogul Kerry Packer publicly endorses views that the Federal Government should deregulate the media and abolish cross-media ownership rules which stop Packer from taking over the Fairfax newspaper group, as well as calling for foreign ownership restrictions to be lifted.
9 April - The Premiers' Conference results in the signing of a new agreement on Commonwealth-State financial relations which offers the states a guaranteed share of tax revenue in the event that the Senate votes for a GST, thereby negating the need for annual negotiations over how tax revenue should be shared.
14 April – A massive hailstorm hits Sydney, with most of the damage being centred on the Eastern Suburbs. It is the second most costliest natural disaster in Australian history, causing $1.7 billion in insured damages.
11 May – The biotechnology industry receives a record $800 million in the federal budget.
21 May – Eight decaying bodies are found in barrels in a disused bank vault north of Adelaide, marking the beginning of the Snowtown murders case, which were Australia's worst ever serial killings. More bodies were found underneath a house in Adelaide on 26 May.
21 June - Senator Mal Colston joins fellow Independent Brian Harradine in supporting the Federal Government's $17 billion sale of the second portion of Telstra (constituting another 16 per cent), allowing the proposed sale to pass through the Senate and become finalised. After the sale, the Government now owns only 50.1 per cent of Telstra.
28 June – The GST bill is passed through the Senate, with the help of most of the Australian Democrats, in exchange for exemptions on fresh food.
2 July - Liberal for Forests, a breakaway single-issue political party, is established in response to the turmoil in the West Australian Liberal Party on the issue of stopping logging in old-growth forests.
5 July - The Commonwealth Director of Public Prosecutions decides to drop the 28 fraud charges against former Senator Mal Colston after receiving two medical specialists' reports which both state that Mr Colston is too ill to face trial, either now or in the future. The decision draws criticism from the Federal Opposition for its timing, due to the fact that Mr Colston was well enough to vote in favour of the Telstra sale the week before.
6 July -
Prime Minister John Howard meets Japan's Prime Minister Keizo Obuchi in Tokyo for trade talks and publicly expresses his disappointment over Indonesia's July 4 attack upon an international aid convoy which he says has placed Indonesia in the international spotlight.
The trial of Federal MP and former West Australian Premier Carmen Lawrence begins in the Perth District Court where she pleads not guilty to three charges of giving false testimony to the Marks Royal Commission.
13 July - ABC-TV's Media Watch programme reveals that radio announcer John Laws had accepted a sponsorship worth $1.2 million from the Banker's Association in return for favourable comments, thereby igniting the cash for comment scandal.
The Sisters of Charity and St Vincent's Hospital reach agreement with the New South Wales Government to run an 18-month clinical trial of a medically supervised heroin injecting room to be established in King's Cross, New South Wales.
18 August - The Supreme Court of Queensland rules that One Nation (Australia) was improperly registered at the 1998 Queensland State Election because it did not have the 500 members needed to register as a political party and the Court also finds that the registration was obtained by fraud and deception.
26 August – The Prime Minister creates controversy when he avoids the use of the word 'sorry' when a motion was tabled in Parliament expressing 'deep & sincere regret that indigenous Australians suffered injustices under the practises of past generations'.
14 November – In response to the growing number of illegal immigrants, most of whom arrived by boat, the government allows police to board vessels in international waters. On 23 November, refugees were barred from seeking asylum in they had lived somewhere else for more than seven days or had the right to live somewhere else.
The Seven Network becomes the first Australian television network to introduce a watermark on its programs, although the watermark is not allowed to be broadcast on news or current affairs programs or Deal Or No Deal from 2004 onwards.
18 March – First day of the Australian Track & Field Championships for the 1998–1999 season, which are held at the Olympic Park in Melbourne, Victoria. The 10,000 metres was conducted at the Zatopek Classic, Melbourne on 5 December 1998. The men's decathlon event was staged at the Hobart Grand Prix on 25–27 February.
25 September – The Kangaroos (19.10.124) defeat Carlton (12.17.89) to win the 103rd VFL/AFL premiership. It is the first all-Victorian grand final since 1995 & the first time the cup has not been won by the Adelaide Crows since 1996.
26 September – A new world record crown for rugby league is set when 107,961 people attend the first National Rugby League grand final held at Stadium Australia. In one of the most memorable & controversial grand finals in history, the Melbourne Storm, in just their second season of existence, defeat the St George Illawarra Dragons 20–18. The final outcome is determined when a penalty try is given to Melbourne's Craig Smith. Melbourne's win means that both the AFL trophy & NRL trophy have been won by teams from the same city for the first time.
3 October – In the third year of the split in the organisation of the Bathurst 1000 the traditional race was held for the last time and won by Paul Morris as the Bathurst 500 was declared after just 310 of the scheduled 500 kilometres due to unrelenting rain. It was a justification for Morris and the BMW team after being disqualified from victory two years ago.
10 October – South Sydney supporters rally through the streets of Sydney to protest against the rationalisation of the NRL to 14 teams for 2000.