  We derive a continuity equation for the Husimi function evolving under a
general non-hermitian Hamiltonian and identify the phase space flow associated
with it. For the case of unitary evolution we obtain explicit formulas for the
quantum flow, which can be written as a classical part plus semiclassical
corrections. These equations are the analogue of the Wigner flow, which
displays several non-intuitive features like momentum inversion and motion of
stagnation points. Many of these features also appear in the Husimi flow and,
therefore, are not related to the negativity of the Wigner function as
previously suggested. We test the exact and semiclassical formulas for a
particle in a double well potential. We find that the zeros of the Husimi
function are saddle points of the flow, and are always followed by a center.
Merging or splitting of stagnation points, observed in the Wigner flow,does not
occur because of the isolation of the Husimi zeros.
