In this paper, a new filtering method for hybrid Markovian switching systems is presented. The method is called the multiple model multiple hypothesis filter ((MH)-H-3 filter). For each hypothesis an (extended) Kalman filter is running. An hypothesis represents a specific model mode sequence history. The proposed method is highly adaptive and flexible. The main feature is that the number of hypotheses that are maintained varies with the 'difficulty' of the situation and that it is adaptive in its computational load. In a representative example it is shown that the M3H filter can outperform the widely used interacting multiple model (IMM) filter, both in terms of accuracy and computational load. The newly proposed filter is an excellent alternative for the widely used and celebrated IMM filter. (c) 2004 Elsevier Ltd. All rights reserved.