  The perturbative QCD corrections to the semileptonic decay width of the tau
lepton are evaluated in the next-next-to-leading order from the contour
integral representation in various renormalization schemes, using numerical
solution of the renormalization group equation for complex energies. A
quantitative estimate of the ambiguities resulting from the freedom of choice
of the renormalization scheme is obtained by taking into account predictions in
all schemes that do not involve large cancellations in the expression for the
scheme invariant combination of the expansion coefficients. The problem of an
optimal choice of the renormalization scheme for the improved perturbative
expression is discussed. A fit of $\Lambda_{\overline{MS}}$ is made using the
available experimental data.
