He decided to defect to Canada because of the limited opportunities in Czechoslovakia under communist rule, which was very strict regarding athletes leaving the country to pursue professional careers elsewhere.

In Pittsburgh, Nedvěd would have the best years of his career on an offensive team featuring superstars Mario Lemieux, Jaromír Jágr, and Ron Francis.

However, Nedvěd would find himself in another major contract dispute, and miss the entire 1997–98 season, instead spending most of the year toiling for lower-level teams in the Czech Republic.

The situation would finally end two months into the season when he was dealt back to the New York Rangers in a deal involving Alexei Kovalev.

Although the team would struggle and miss the playoffs every year through this stretch, Nedvěd would be a consistent offensive performer, leading the Rangers in scoring twice and finishing second on another occasion.

In 2000–01, playing with Jan Hlaváč and Radek Dvořák – a trio dubbed the 'Czech Mates' – he had the second-best season of his career, finishing with 32 goals and 78 points.

The 2006–07 season again started poorly for Nedvěd, and he was placed on waivers on October 18 following a 9–1 loss to the Buffalo Sabres, and was assigned to the American Hockey League (AHL) for the first time in his career.

After bouncing between the NHL and AHL for the next two months, Nedvěd was claimed on re-entry waivers by the Edmonton Oilers, who hoped he could provide the same sort of spark he did when acquired in 2004.

[2] On July 31, 2008, Nedvěd, attempting to make an NHL comeback, was invited to the New York Rangers training camp on a tryout basis.

On March 13, 2014, Nedvěd played his last career game with Bílí Tygři Liberec in a 6–2 home loss against the HC Vítkovice Steel.

In early 2006, when playing for the Phoenix Coyotes, Nedvěd asked for a trade to an Eastern Conference team to be closer to Vařeková who worked primarily in New York City.