[1] Pálóczi first made his mark in international athletics at the 1983 European Indoor Championships in Budapest.
With a jump of 7.90 metres he won the silver medal, five centimetres behind compatriot László Szalma.
[6] He became the Hungarian long jump champion in 1984, 1986 and 1990, rivalling with László Szalma and Csaba Almási.
He became the Hungarian triple jump champion in 1988, 1989, 1990, 1993 and 1994; his main rivals were Béla Bakosi, Tibor Ordina and Zsolt Czingler.
[9] Internationally he competed in the triple jump event at the 1993 World Championships, but with only 15.89 metres he finished near the bottom of the list, and did not reach the final.