In this paper, an approach to autonomous learning of a multi-model system from streaming data, named ALMMo, is proposed. The proposed approach is generic and can easily be applied also to probabilistic or other types of local models forming multi-model systems. It is fully data-driven and its structure is decided by the nonparametric data clouds extracted from the empirically observed data without making any prior assumptions concerning data distribution and other data properties. All meta-parameters of the proposed system are obtained directly from the data and can be updated recursively, which improves memory- and calculation-efficiency of the proposed algorithm. The structural evolution mechanism and online data cloud quality monitoring mechanism of the ALMMo system largely enhance the ability of handling shifts and/or drifts in the streaming data pattern. Numerical examples of the use of ALMMo system for streaming data analytics, classification and prediction are presented as a proof of the proposed concept.