Since her own birth and until the birth on 20 May 1967 of her brother Pavlos, Princess Alexia was heiress presumptive to the throne of Hellenes, then an extant monarchy. The succession law of Greece was not a Salic one, instead it was effectively similar with the ones of the United Kingdom and Spain.
On 9 July 1999 Princess Alexia married Carlos Morales Quintana, an architect and a champion yachtsman, at St. Sophia Cathedral, London.  The bride wore a gown by the Austrian designer Inge Sprawson.  Her attendants were her sister Princess Theodora, her niece Princess Maria Olympia, and Princess Mafalda, daughter of Prince Kyril of Bulgaria.
The couple has four children:
Arrietta Morales y de Grecia (born 24 February 2002 in Barcelona)
Ana María Morales y de Grecia (born 15 May 2003 in Barcelona)
Carlos Morales y de Grecia (born 30 July 2005 in Barcelona)
Amelia Morales y de Grecia (born 26 October 2007 in Spain)