Evolution of winding strings in spacetimes with cycles whose proper lengths depend on time is examined. It was established earlier that extended objects wrapping the shrinking dimension in compactified Milne spacetime enjoy classically nonsingular evolution. Extensions of this observation to other spacetimes are discussed.

PACS numbers: 11.25.--w, 11.27.+d, 98.80.Bp, 98.80.--k