Ladkin and Maddux [LaMa87] showed how to interpret the calculus of time intervals defined by Allen [AZ2831 in terms of representations of a particular relation algebra, and proved that this algebra has a unique countable representation up to isomorphism. In this paper, we . consider the algebra An of n-intervals, which coincides with Allen's algebra for n=2, and prove that An has a unique countable representation up to isomorphism for