We propose a new class of soft-input soft-output demodulation schemes for multiple-input multiple-output (MIMO) channels, based on the sequential Monte Carlo (SMC) framework under both stochastic and deterministic settings. By exploiting the artificial sequential structure of the existing simple BLAST detection method based on nulling and cancellation, the proposed algorithms achieve an error probability performance that is orders of magnitude better than the traditional BLAST detection schemes while maintaining a low computational complexity. In fact, the new methods offer performance comparable with that of the sphere decoding algorithm, without attendant increase in complexity. Computer simulation results are provided to demonstrate the performance of the proposed algorithms.