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The multilevel structure of the N-QAM modulation constellations is exploited to significantly reduce the complexity of the sequential Gaussian approximation (SGA) algorithm for near optimal symbol detection in spatial multiplexing multiple- input multiple-output (MIMO) system. We propose two multilevel SGA algorithms (MSGA) which are based on depth- first search (DFS) and breadth-first search (BFS) respectively. Additionally, an important methodological contribution to this multilevel technique is proposed where the mismatch between the pseudo symbols and the true symbols is taken into consideration for the computation of posterior probabilities of symbol combinations. We justify this from a theoretical perspective as well as with numerical results. Simulation results show that the performance of the two proposed multilevel algorithms can approach that of the optimal a posteriori probability (APP) detector while its total computation cost is at most 81% and 48% of that of the original SGA algorithm for 16QAM and 64QAM modulation MIMO systems with 4 transmit/receive antennas respectively.