  We study the potential of a future $e^+e^-$ collider for the search of
anomalous gamma t t bar and Z t t bar couplings, assuming that CP-invariance
holds. This is done in a model-independent way, considering that all six
possible couplings do appear. Two experimental situations are envisaged, with
and without electron beam polarization. Observability limits in the form of
domains in the 6-dimensional parameter space are established. Illustrations for
specific constrained models are also presented and implications for new physics
searches are discussed.
