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In this paper, we present the ergodic capacity limits of time-varying multiple-input multiple-output (MIMO) channels in flat fading and frequency-selective fading environments. By using a nonstationary method, called generalized water-filling algorithm (GWFA), the transmitted power is optimally allocated over all the channel states in three dimensions including space, time and frequency. Therefore, the highest capacity (i.e., capacity limit) of time-varying MIMO channels is obtained. Compared with the conventional water-filling algorithm, GWFA can achieve higher capacity via more efficient computation.