We consider a boson field φ{symbol}(x) under an interaction of the form {Mathematical expression}V(φ{symbol}(x))dx, where V(α) is a bounded continuous real function of a real variable α. If V(α) has a uniformly continuous and bounded first derivative, we prove that the Heisenberg picture field exists as weak limits of the Heisenberg picture fields corresponding to the cut-off interaction. © 1969 Springer-Verlag.