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This paper presents precoding design for error-rate improvement in closed-loop multiuser orthogonal space-time block-coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) downlink, where both mean feedback and covariance feedback are available. We derive adaptive linear precoding and nonlinear Tomlinson-Harashima precoding (THP) over a transmit-antenna-correlated, frequency-selective fading MIMO channel with estimation errors and feedback delay. In our precoder, mean-feedback precoding or covariance-feedback precoding, is adaptively chosen at the user terminal. The maximum achievable signal-to-noise power ratio (SNR) is used as the precoding-mode selection criterion. Each user calculates the selection metric and decides whether mean feedback is necessary. We confirm the intuition that mean-feedback precoding offers BER gains over covariance-feedback precoding when mean feedback becomes sufficiently accurate. Our adaptive precoding outperforms either mean-feedback precoding or covariance-feedback precoding in multiuser OSTBC OFDM, and considerably reduces the bit error rate (BER). Non-linear adaptive precoding is shown to outperform linear adaptive precoding.