One major challenge to implement orthogonal frequency division multiplexing (OFDM) systems over doubly selective channels is the non-negligible intercarrier interference (ICI), which significantly degrades the system performance. Existing solutions to cope with ICI include zero-forcing (ZF), minimum mean square error (MMSE) and other linear or nonlinear equalization methods. However, these schemes fail to achieve a satisfactory tradeoff between performance and computational complexity. To address this problem, in this paper we propose two novel nonlinear ICI cancellation techniques, which are referred to as parallel interference cancelation (PIC) and hybrid interference cancelation (HIC). Taking advantage of the special structure of basis expansion model (BEM) based channel matrices, our proposed schemes enjoy low computational complexity and are capable of cancelling ICI effectively. Moreover, since the proposed schemes can flexibly select different basis functions and be independent of the channel statistics, they are applicable to practical OFDM based systems such as DVB-T2 over doubly selective channels. Theoretical analysis and simulation results both confirm their performance-complexity advantages in comparison with some existing methods.