  This paper studies the electroweak production of all possible four-fermion
states in $e^+e^-$ collisions with non-standard triple gauge boson couplings.
All $CP$ conserving couplings are considered. It is an extension of the methods
and strategy, which were recently used for the Standard Model electroweak
production of four-fermion final states. Since the fermions are taken to be
massless the matrix elements can be evaluated efficiently, but certain phase
space cuts have to be imposed to avoid singularities. Experimental cuts are of
a similar nature. With the help of the constructed event generator a number of
illustrative results is obtained for $W$-pair production. These show on one
hand the distortions of the Standard Model angular distributions caused by
either off-shell effects or initial state radiation. On the other hand, also
the modifications of distributions due to anomalous couplings are presented,
considering either signal diagrams or all diagrams.
