  We study joint free cumulants of u_t and u_t^{*}, where u_t is a free unitary
Brownian motion at time t. We determine explicitly some special families of
such cumulants. On the other hand, for a general joint cumulant of u_t and
u_t^{*}, we "calculate the derivative" for t going to infinity, when u_t
approaches a Haar unitary. In connection to the latter calculation we put into
evidence an "infinitesimal determining sequence" which naturally accompanies an
arbitrary R-diagonal element in a tracial *-probability space.
