A trajectory of a destination-directed moving object (e.g. an aircraft from an origin airport to a destination airport) has three main components: an origin, a destination, and motion in between. We call such a trajectory that end up at the destination destination-directed trajectory (DDT). A class of conditionally Markov (CM) sequences (called CML) has the following main components: a joint density of two endpoints and a Markov-like evolution law. A CML dynamic model can describe the evolution of a DDT but not of a guided object chasing a moving guide. The trajectory of a guided object is called a guided trajectory (GT). Inspired by a CML model, this paper proposes a model for a GT with a moving guide. The proposed model reduces to a CML model if the guide is not moving. We also study filtering and trajectory prediction based on the proposed model. Simulation results are presented.