Filter bank multi-carrier (FBMC) is a modulation technique with enhanced spectral properties compared with orthogonal frequency division multiplexing (OFDM). In this letter, we investigate the performance degeneration of OFDM and FBMC in doubly-selective channels, that is, time-selectivity and frequency-selectivity. For that, we derive closed-form bit error probability (BEP) expressions for arbitrary linear modulation methods based on one-tap equalizers, with OFDM and FBMC being special cases, covered by our general BEP expressions. We validate our calculations by Monte Carlo simulations and investigate the BEP error if the interference is approximated as Gaussian noise.