Adaptive equalization of wireless systems operating over time-varying and frequency-selective multiple-input multiple-output (MIMO) channels is considered. A novel equalization structure is proposed, which comprises a cascade of decision feedback equalizer (DFE) stages, each one detecting a single stream. The equalizer filters, as well as the ordering by which the streams are extracted, are updated based on the minimization of a set of least squares (LS) cost functions in a BLAST-like fashion. To ensure numerically robust performance of the proposed algorithm, Cholesky factorization of the equalizer input autocorrelation matrix is applied. Moreover, after showing that the equalization problem possesses an order recursive structure, a computationally efficient scheme is developed. A variation of the method is also described, which is appropriate for slow time-varying conditions. Theoretical analysis of the equalization problem reveals an inherent numerical deficiency, thus justifying our choice of employing a numerically robust algebraic transformation. The performance of the proposed method in terms of convergence, tracking, and bit error rate (BER) is evaluated through extensive computer simulations for time-varying and wideband channels.