The concept of special grain boundary dislocations (as distinct from crystal dislocations) has been used to study the mechanism of the passage of crystal dislocations through tilt boundaries in the simple cubic and bcc systems. It is shown that the Burgers vector of a grain boundary dislocation is not arbitrary but should be a vector belonging to a restricted set defined in terms of the translation vectors of the two grains separated by the grain boundary. It is next shown that a grain boundary dislocation can be constructed in a bicrystal in the same manner as a crystal dislocation in a single crystal. The properties of these dislocations in a bicrystal are studied. It is shown that a crystal dislocation can pass through a tilt boundary without altering its over‐all structure by first dissociating into partials whose Burgers vectors are integral units of those of the grain boundary dislocations defined for the bicrystal. The principles involved are illustrated by means of an example each in the simple cubic and bcc systems.