  Let $F: T^{n} \times I \to T^{n}$ be a homotopy on a n-dimensional torus. The
main purpose of this paper is to present a formula for the one-parameter
Nielsen number $N(F)$ of $F$ in terms of induced homomorphism. If $L(F)$ is the
one-parameter Lefschetz class of $F$ then $L(F)$ is given by $L(F) = \pm
N(F)\alpha,$ for some $\alpha \in H_{1}(\pi_{1}(T^{n}),\mathbb{Z}).$
