In this paper we propose a blind data detection principle for space-time coding systems in time-varying fading channels. To solve the ambiguity problem in the blind detection, we consider semi-blind schemes for systems with (1) the spacetime trellis coding (STTC) and (2) a trellis coded modulation (TCM) cascaded with a space-time block coding (STBC). We develop our algorithm based on the per-survivor processing (PSP) on the trellis, and model the channel variation by a polynomial of time indices. A least-squares-fitting approach is applied to determine the coefficients of the polynomial. Our algorithm needs not to know the channel statistics like correlation functions and signal-to-noise ratio (SNR). Since the pilot density is low in the data streams of the semi-blind scheme, the transmission rate can be near that of pure blind schemes.