The orbital evolution of comets with high values of the Tisserand constant is studied for a time interval of 800 years. Scenarios of dynamical evolution are obtained for 85 comets. Particular features of the orbital evolution of the comets of this class are singled out. The orbits of all comets are tangent to the orbit of Jupiter and have a steadily low inclination. For 80% of comets, the evolution scenario includes a timespan in which the comets move in low-eccentricity orbits. The possibility is analyzed of a change in the Tisserand constant and of a transition of the comet to be controlled by other giant planets.
