Gullikson and his twin brother Tom attended Northern Illinois University . After completing his studies, he first worked as a tennis coach. After playing at satellite tournaments, his breakthrough came in 1977 with three individual titles. For this he was named Newcomer of the Year by the ATP . In addition, he was twice in a double final with his brother Tom. In 1978 he won his fourth and final single title in Johannesburg and three double titles alongside his brother. Of the total of 15 double titles in his career, he won ten together with his brother. He reached his highest world rankings in 1979 with position 15 in singles and 1983 with position 3 in doubles.
His best individual result in a Grand Slam tournament was the quarter-finals at Wimbledon in 1979. In the doubles competition, he reached the Wimbledon final with his brother in 1983, but they were subject to Peter Fleming and John McEnroe in three sets. He was also in the semi-finals of the Australian Open and the US Open .
After his professional career, he became a tennis coach. Among others, he looked after Martina Navrátilová , Mary Joe Fernández and Aaron Krickstein . Later he looked after the then world number one Pete Sampras . At the 1995 Australian Open, Gullikson, who was later diagnosed with a brain tumor, suffered a faint attack . Sampras therefore burst into tears during his game against Jim Courier . Gullikson died in May 1996.