  We derive a kinetic theory for a spin-1/2 Bose-condensed gas of two-level
atoms at finite temperatures. The condensate dynamics is described by a
generalized Gross-Pitaevskii equation for the two-component spinor order
parameter, which includes the interaction with the uncondensed fraction. The
noncondensate atoms are described by a quantum kinetic equation, which is a
generalization of the spin kinetic equation for spin-polarized quantum gases to
include couplings to the condensate degree of freedom. The kinetic equation is
used to derive hydrodynamic equations for the noncondensate spin density. The
condensate and noncondensate spins are coupled directly through the exchange
mean field. Collisions between the condensate and noncondensate atoms give rise
to an additional contribution to the spin diffusion relaxation rate. In
addition, they give rise to mutual relaxation of the condensate and
noncondensate due to lack of local equilibrium between the two components.
