The problem of adaptive decoding of space-time trellis codes on time-variant wireless channels is considered. We show that per-survivor processing (PSP) can be adopted to obtain approximated adaptive maximum-likelihood sequence detection (MLSD) of space-time trellis codes when there is no periodically inserted orthogonal pilot sequence. Then we propose a self-tuning least mean square (LMS)-based PSP decoder and a second-order LMS-based one. The former has the advantage that there are only fading rate-independent parameters to be predetermined, while the latter can offer fairly good performance on moderately fast time-varying channels.