This paper addresses the issue of blind multiple-input multiple-output (MIMO) demodulation of communication signals, with time-varying channels and in an interception context. A new adaptive-blind source separation algorithm, which is based on the implementation of the Multimodulus cost function by analytical methods, is proposed. First a batch processing analysis is performed; then an adaptive implementation of the (Analytical Multi-Modulus Algorithm) AMMA and its simplified version named (Analytical Simplified Constant Modulus Algorithm) ASCMA is detailed. These algorithms, named adaptive-AMMA and adaptive-ASCMA, respectively, are compared with the adaptive (Analytical Constant Modulus Algorithm) ACMA and the MMA (Multi-Modulus Algorithm). The adaptive-AMMA and adaptive-ASCMA achieve a lower residual intersymbol interference and bit error rate than those of the adaptive-ACMA and MMA.