Summary: In this paper, a novel statistical model based on 2-D HMMs for image recognition is proposed. Recently, separable lattice 2-D HMMs (SL2D-HMMs) were proposed to model invariance to size and location deformation. However, their modeling accuracy is still insufficient because of the following two assumptions, which are inherited from 1-D HMMs: i) the stationary statistics within each state and ii) the conditional independent assumption of state output probabilities. To overcome these shortcomings in 1-D HMMs, trajectory HMMs were proposed and successfully applied to speech recognition and speech synthesis. This paper derives 2-D trajectory HMMs by reformulating the likelihood of SL2D-HMMs through the imposition of explicit relationships between static and dynamic features. The proposed model can efficiently capture dependencies between adjacent observations without increasing the number of model parameters. The effectiveness of the proposed model was evaluated in face recognition experiments on the XM2VTS database.