The aim of this paper is to follow up the program set in [LR85, Rau92], i.e., to show the existence of nontrivial group actions ("symmetries") on certain classes of manifolds. More specifically, given a manifold X with submanifold F, I would like to construct nontrivial actions of cyclic groups on X with F as fixed point set. Of course, this is not always possible, and a list of necessary conditions for the existence of an action of the circle group T = S1 on X with fixed point set F was established in [Rau92]. In this paper, I assume that the rational homotopy types of F and X are related by a deformation in the sense of [All78] between their (Sullivan) models as graded differential algebras (cf. [Sul77, Hal83]). Under certain additional assumptions, it is then possible to construct a rational homotopy description of a T-action on the complement $X \backslash F$ that fits together with a given T-bundle action on the normal bundle of F in X. In a subsequent paper [Rau94], I plan to show how to realize this T-action on an actual manifold Y rationally homotopy equivalent to X with fixed point set F and how to "propagate" all but finitely many of the restricted cyclic group actions to X itself.