Linear adaptive filters are often used for Acoustic Echo Cancellation (AEC) but sometimes fail to perform well in notebook computers and inexpensive telephony devices. Low-quality speakers and poorly-designed enclosures that produce vibrations often generate harmonic distortion, and this nonlinear effect degrades the performance of linear AEC algorithms considerably. In this work, we present a new AEC architecture that consists of a linear, subband adaptive AEC filter followed a nonlinear residual echo suppression (RES) stage specifically designed to address harmonic distortion. In addition to suppressing the residual echo in the primary subband, the proposed model also suppresses the residual echo in a window of bands surrounding the higher order harmonics. Results show considerable improvement over other proposed algorithms, and the new algorithm has much lower implementation costs compared to nonlinear AEC models based on Volterra filters and a previously proposed, nonlinear residual echo suppression algorithm.