  We describe a detailed study of the process $e^+e^- \to \ell\nu_\ell q
\bar{q}$ and the measurement of tri-linear gauge boson couplings (TGV's) at
LEP200 and at a 500~GeV and 1~TeV NLC. We included all tree level Feynman
diagrams contributing to the four-fermion final states including gauge boson
widths and non-resonance contributions. We employed a maximum likelihood
analysis of a five dimensional differential cross section of angular
distributions. This approach appears to offer an optimal strategy for
measurement of TGV's. LEP200 will improve existing measurements of TGV's but
not enough to see loop contributions of new physics. Measurements at the NLC
will be roughly 2 orders of magnitude more precise which would probe the
effects of new physics at the loop level.
