  We address the issue of coupling variables which are essentially classical to
variables that are quantum. Two approaches are discussed. In the first (based
on collaborative work with L.Di\'osi), continuous quantum measurement theory is
used to construct a phenomenological description of the interaction of a
quasiclassical variable $X$ with a quantum variable $x$, where the
quasiclassical nature of $X$ is assumed to have come about as a result of
decoherence. The state of the quantum subsystem evolves according to the
stochastic non-linear Schr\"odinger equation of a continuously measured system,
and the classical system couples to a stochastic c-number $\x (t)$ representing
the imprecisely measured value of $x$. The theory gives intuitively sensible
results even when the quantum system starts out in a superposition of
well-separated localized states. The second approach involves a derivation of
an effective theory from the underlying quantum theory of the combined
quasiclassical--quantum system, and uses the decoherent histories approach to
quantum theory.
