Alsup made his CART debut at the &lt;a href="1979%20Arizona%20Republic%20/%20Jimmy%20Bryan%20150"&gt;Arizona Republic/Jimmy Bryan 150&lt;/a&gt; at Phoenix International Raceway driving the #41 WASP Racing Mclaren-Offenhauser for WASP Racing starting twenty fourth (last) and finishing eleventh. He attempted to qualify for the Indianapolis 500, first driving the #67 WASP Racing McLaren-Offenhauser, but the car was not fast enough to make a qualifying run. He then attempted the #19 Sta-On Eagle 74-Offenhauser for Gehlhausen Racing but the engine failed. The final car he attempted to qualify was the #68 CAM 2 Motor Oil Penske PC7-Cosworth DFX for Team Penske. He qualified for the race but USAC officials ruled that the car used the engine from Penske teammate Bobby Unser's car and Alsup was disqualified.