  We discuss conditions under which expectation values computed from a complex
Langevin process $Z$ will converge to integral averages over a given complex
valued weight function. The difficulties in proving a general result are
pointed out. For complex valued polynomial actions, it is shown that for a
process converging to a strongly stationary process one gets the correct answer
for averages of polynomials if $c_{\tau}(k) \equiv E(e^{ikZ(\tau)}) $ satisfies
certain conditions. If these conditions are not satisfied, then the stochastic
process is not necessarily described by a complex Fokker Planck equation. The
result is illustrated with the exactly solvable complex frequency harmonic
oscillator.
