The collisions of two simultaneously generated impulses in the giant axons of both earthworms and lobsters propagating in orthodromic and antidromic direction are investigated. The experiments have been performed on the extracted ventral cords of Lumbricus terrestris and the abdominal ventral cord of a lobster, Homarus americanus, by using external stimulation and recording. The collision of two nerve impulses of orthodromic and antidromic propagation did not result in the annihilation of the two signals, contrary to the common notion that is based on the existence of a refractory period in the well-known Hodgkin-Huxley theory. However, the results are in agreement with the electromechanical soliton theory for nerve-pulse propagation, as suggested by Heimburg and Jackson [On Soliton Propagation in Biomembranes and Nerves, Proc. Natl. Acad. Sci. U.S.A. 102, 9790 (2005).].