After the collapse of Mastercard-Lola, Sospiri turned his attention to the Indy Racing League IndyCar Series where he signed on with Team Scandia to race in the 1997 Indianapolis 500. Sospiri put the Scandia Dallara-Oldsmobile third on the starting grid in his first IndyCar start and finished 17th in the race. Later that season he finished second at the New Hampshire Motor Speedway. He finished 21st in the championship despite only competing in six of the ten races of the 1996-1997 season. In 1998 Sospiri was brought on to Dan Gurney's All American Racers team as a late-season replacement for P. J. Jones and drove in the final four races of the season for the team. He had a best finish of 15th at both Houston and Surfers Paradise and failed to finish in the points as the team's struggles continued. He was named to an ISM Racing entry for the 1999 Indianapolis 500 but the car was driven by Brian Tyler instead, who failed to qualify.