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The performance of an automatic frequency control (AFC) loop is investigated using two measures, the mean time to loss of lock and the average switching rate. The AFC is considered to operate in fading while a single interferer is also present at its input. Channels are modeled using independent non-identically distributed Rayleigh, Rician and Nakagami-m fading while the special case of independent identically distributed channels is also considered. Closed-form expressions and integral form formulas are derived for the general case of modulated signals as well as important special cases of similar modulations and unmodulated signals. The considered scenarios include previous results from the literature as special cases. Corresponding numerical examples are provided and discussed to illustrate the performance of an AFC in such scenarios.