Spreading of a liquid drop to equilibrium on a soft, viscoelastic substrate can be much slower than on an equivalent hard material due to energy dissipation in the deformed solid near the wetting front : the liquid surface tension creates a "wetting ridge" which moves with the triple line. When a film of nonwetting liquid is applied to a solid surface, dry patches may nucleate and grow. In the case of a viscoelastic solid, it is shown that the speed of dry patch enlargement is also largely moderated by energy dissipation brought about by the strain cycle of the solid in the triple-line region. The speed of triple-line recession is shown, both theoretically and experimentally, to be constant, in agreement with the capillary regime of the same process on a hard solid, but the viscoelastically controlled spreading rate is about an order of magnitude smaller.