  We analyze the perturbative and parametric stability of the QCD predictions
for the azimuthal asymmetries in heavy quark leptoproduction. At leading order,
the $\cos \phi$ asymmetry vanishes whereas the $\cos 2\phi$ one is of leading
twist and predicted to be about 15% at energies sufficiently above the
production threshold. We calculate the NLO soft-gluon corrections to
$\phi$-dependent leptoproduction to the next-to-leading logarithmic accuracy.
The soft-gluon approximation provides a good description of the available exact
NLO results at $Q^{2}\lesssim m^{2}$. Our analysis shows that, contrary to the
production cross sections, the $\cos 2\phi$ asymmetry is practically
insensitive to soft radiation for $Q^{2}\lesssim m^{2}$ at energies of the
fixed target experiments. We conclude that the $\cos 2\phi$ asymmetry is well
defined in pQCD: it is stable both perturbatively and parametrically, and
insensitive (in the case of bottom production) to nonperturbative
contributions. Measurements of the azimuthal asymmetries would provide an
excellent test of pQCD applicability to heavy flavor production.
