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The main result of this paper states that if $$F: T \times I \rightarrow T$$ is a homotopy on 2-dimensional torus and $$\pi _{1}(T,x_{0}) = <u,v|[u,v]=1>$$, then the one-parameter Lefschetz class L(F) of F is given by $$\begin{aligned} L(F) = \pm N(F)\alpha , \end{aligned}$$where N(F) is the one-parameter Nielsen number of F,  and $$\alpha = [u] \in H_{1}(\pi _{1}(T),\mathbb {Z})$$.

One-parameter Lefschetz class of homotopies on torus