"This was a good match for me, it was a good way to start," he said. "The first match is the one you worry about, especially if you've never played the opponent before."
"The conditions are different here (from Madrid) and I knew there had to be some adjustments. I was hoping they would come fast and I was up early so that helped me relax."
Playing in Stockholm for the first time in 10 years, the top seed was unthreatened by the 107th-ranked Vliegen in the first set, the Belgian making too many unforced errors.
He broke Vliegen to 2-1 and again to 5-2 in the opening set before serving it out.
Vliegen raised his game in the second set and broke the American in the eighth game to level 4-4 but Agassi shrugged it off by breaking the Belgian to love and then converted 6-4.
"In the second set it got more competitive, he played much better and he broke to four all. Then I played a really good game to break him," Agassi said.
In the second round the 34-year-old American takes on Swedish doubles specialist Jonas Bjorkman. Bjorkman overcame Australian Wayne Arthurs 4-6, 6-4, 6-4.
WITH FAMILY
"The next match is going to be even tougher," said Agassi. "We've played each other a couple of times ... Jonas is a talented player. He'll have the home crowd advantage."
Agassi, who has no plans of retiring from tennis in 2005, has come to Sweden with his wife Steffi Graf and their children.
"It's difficult to travel with the family, but it's a better alternative than not to do it. I don't think I would play if I couldn't," he said.
Earlier in the day Belgian Olivier Rochus became the first player through to the quarter-finals when he beat qualifier Janko Tipsarevic of Serbia & Montenegro 6-4, 7-5 in a second round match.
After clinching the first set Rochus climbed back from 4-1 to 4-4 in the second and then broke Jankovic again in the eleventh game. The Belgian finished in style, serving out to love to wrap up the match.
Rochus was joined in the quarters by former Australian Open champion Thomas Johansson of Sweden, who beat his sixth-seeded compatriot Robin Soderling 1-6, 7-6, 6-4 in a close meeting.
Johansson takes on Romanian third seed Andrei Pavel, who beat Czech Michal Tabara 6-3, 3-6, 6-3.
