Stimulus-frequency otoacoustic emissions (SFOAEs) are generated by coherent reflection of forward traveling waves by perturbations along the basilar membrane. The strongest wavelets are backscattered near the place where the traveling wave reaches its maximal amplitude (tonotopic place). Therefore, the SFOAE group delay might be expected to be twice the group delay estimated in the cochlear filters. However, experimental data have yielded steady-state SFOAE components with near-zero latency. A cochlear model is used to show that short-latency SFOAE components can be generated due to nonlinear reflection of the compressor or suppressor tones used in SFOAE measurements. The simulations indicate that suppressors produce more pronounced short-latency components than compressors. The existence of nonlinear reflection components due to suppressors can also explain why SFOAEs can still be detected when suppressors are presented more than half an octave above the probe-tone frequency. Simulations of the SFOAE suppression tuning curves showed that phase changes in the SFOAE residual as the suppressor frequency increases are mostly determined by phase changes of the nonlinear reflection component.