We study the continuous frequency spectrum management problem for the two-user Gaussian interference channel. We consider a successive interference cancellation scheme between the two receivers. In this model, receiver 1 decodes user 1 and passes the decoded bits to receiver 2 which in turn cancels the interference from user 1. We analytically determine the optimal power spectral density for users 1 and 2 for an asymmetric flat fading channel. We show when frequency division multiplexing (FDM) is optimal. We also show when frequency sharing with cancellation dominates FDM. Moreover we formulate the frequency selective case as a convex optimization problem. Both the sum power constraint and the individual power constraint are analyzed. As opposed to the linear case (no cancellation), only two pure spectrum allocation schemes are optimal when we have interference cancellation: either sharing or orthogonal. No mixed scheme is optimal. The two regions are determined by the channel conditions and are independent of the power constraints imposed. We also notice that the FDM region shrinks and the spectral efficiency increases as a result of introducing cancellation.