  We show that the Truncated Wigner Approximation developed in the flat
phase-space is mapped into a Lindblad-type evolution with an indefinite metric
in the space of linear operators. As a result, the classically evolved Wigner
function corresponds to a non-positive operator $\hat{R}(t)$, which does not
describe a physical state. The rate of appearance of negative eigenvalues of
$\hat{R}(t)$ can be efficiently estimated. The short-time dynamics of the Kerr
and second harmonic generation Hamiltonains are discussed.
