The purpose of this paper is to study the behavior of the Kobayashi and Carath6odory pseudodistances and (infinitesimal) pseudometrics near the origin of complete circular domain in a complex locally convex separate topological vector space. Let V be a locally convex separate topological vector space over the field C of the complex numbers. We recall that a domain D c V (that is, a connected open subset of V) is complete circular if CzeD whenever z e D and C~C, ICI < 1. For any domain D c V we denote by k o and c o respectively the Kobayashi and Carath6odory distance functions, and by x D and ?o the corresponding (infinitesimal) metrics. For the definitions and the principal properties of these objects see [4]. Our first result is the following: