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Let F be a compact 2-manifold and 1 the closed unit interval. Let a and fl be arcs embedded in Fx I such that ac and fl meet the boundary of Fx I in the boundary of cc and fl respectively. Then we give necessary and sufficient conditions for the existence of an ambient isotopy, constant on the boundary of Fxl, moving cc to fl. We also obtain ambient isotopies of families of arcs properly embedded in Fx I.

Isotopy equivalence classes of normal arcs in $F\times I$