In this paper, we propose a maximum-likelihood sequence estimation (MLSE) procedure for transmission over rapidly time-varying channels. The time-varying channel is approximated using the basis expansion model (BEM). Using the BEM allows for an efficient implementation of the Viterbi algorithm (VA). This stems from the fact that with the BEM the time-varying channel is approximated over a window of size N by a bank of time-invariant filters, and the time-variation of each filter is captured by a corresponding time-varying complex exponential basis function. Therefore, a time-invariant state diagram of each filter is first constructed and then used to update the branch metrics at every recursion. This can be applied for single carrier transmission as well as for multi-carrier transmission.