Since her own birth and until the birth on 20 May 1967 of her brother Pavlos, Princess Alexia was heir 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) her godparents are Princess Theodora of Greece (maternal aunt); Maria Teresa Morales (paternal aunt); Infanta Cristina of Spain (her mother's paternal first cousin) and Manuel Cabrera (her father's friend)
Ana María Morales y de Grecia (born 15 May 2003 in Barcelona) her godparents are Pavlos, Crown Prince of Greece (maternal uncle) and Alejandro Morales (paternal uncle)
Amelia Morales y de Grecia (born 26 October 2007 in Spain) her godparents are Prince Philippos of Greece and Denmark (paternal uncle) and Princess Alexandra of Sayn-Wittgenstein-Berleburg (her mother's cousin)