Many phenomena in molecular transport junctions involve transitions between electronic states of the molecular wire, and, therefore, cannot be described adequately using the Landauer picture. We present a model for cotunneling processes in molecular wires. These are coherent second-order processes that can be observed at low temperatures. As an example, we consider the STM-induced dissociation of acetylene. The large voltage threshold for dissociation observed experimentally is naturally accounted for within the cotunneling model.