  We calculate the relaxational dynamical critical behavior of systems of
$O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the
minimal subtraction scheme in two loop order. The three different bicritical
static universality classes previously found for such systems correspond to
three different dynamical universality classes within the static borderlines.
The Heisenberg and the biconical fixed point lead to strong dynamic scaling
whereas in the region of stability of the decoupled fixed point weak dynamic
scaling holds. Due to the neighborhood of the stability border between the
strong and the weak scaling dynamic fixed point corresponding to the static
biconical and the decoupled fixed point a very small dynamic transient
exponent, of $\omega_v^{{\cal B}}=0.0044$, is present in the dynamics for the
physically important case $n_\|=1$ and $n_\perp=2$ in $d=3$.
