We consider the contributions of the extra gauge boson Z′ to the like sign τ production processes e−γ → e+(μ+)τ−τ−, induced by the tree-level flavor changing interactions. Since these rare production are far below the observable level in the Standard Model and other popular new physics models such as the minimal supersymmetric model, we find that, in the topcolor-assisted technicolor models, the Z′ can give significant contributions to these processes, and with reasonable values of the parameters, the cross section σ can reach several tens of fb and may be detected at the eγ collisions.