This paper deals with a model hyperbolic equation in \( {\mathbb R}^{2} \) with nonlocal term and a nonlinear term of the type \( f(m) \). The equation mentioned above describes the damped motion of an unbounded one dimensional viscoelastic body on which a kind of attracting force is acting. The author reduces the study of this equation to the investigation of a first order integro-differential system having initial-history data. In Theorem 1 a local existence in time result is shown. In Theorem 2 a global existence result is announced and it is proved the uniform stability in \( x \) of the constant solution for \( t \rightarrow \infty \).