We consider the problem of tracking multiple maneuvering targets in clutter using switching multiple target motion models. A suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach and the joint probabilistic data association (JPDA) technique to a Markovian switching system. A suboptimal fixed-lag smoothing algorithm is developed by applying the IMM and the JPDA approaches to a state-augmented system. The algorithms are illustrated via a simulation example involving tracking of two highly maneuvering targets.