The authors study a system of differential equations with impulses of the form
where is in the -dimensional torus , , is an -dimensional closed submanifold of , the functions , , and are continuous and -periodic in , , . The dynamics of the system (1) is as follows. Between two successive meetings of the point with the motion proceeds along the trajectory of the system , . When the point meets it is momentarily transfered to the point . For system (1) sufficient conditions are obtained for the existence of an integral manifold of the form , , . Some continuous properties of are investigated.