This paper studies the tracking performance of adaptive filters operating in the presence of two sources of nonstationarities: carrier frequency offsets and random channel variations. Both impairments are common in digital communications due to mismatches between transmitter and receiver carrier generators and channel fading. The paper derives expressions for the mean-square error and shows how filter performance is degraded under such nonstationary conditions. Selections of step sizes for optimal tracking performance are derived, different adaptive algorithms are compared, and supporting simulation results are provided.