In multidimensional case we give an extension of the Lindelöf-Gehring-Lohwater theorem involving two paths. A classical theorem of Lindelö f asserts that if f is a function analytic and bounded in the unit disc U which has the asymptotic value L at a point ξ ε ∂U then it has the angular limit L at ξ. Later Lehto and Virtanen proved that a normal function f has at most one asymptotic value at any given point ξ ε ∂U. Subsequently, the hypothesis of the existence of an asymptotic value has been weakend by Gehring and Lohwater. In this paper we extend their results to the higher dimensional case.