  We calculate finite mass corrections to leptonic decay constants in HQET
using QCD sum rules. The results are given to two--loop accuracy including
renormalization group analysis. The contribution of unknown two--loop anomalous
dimension matrix--elements is estimated. We find that the $1/m_Q$ corrections
to $f_P$, the decay constant of a pseudoscalar meson, amount $-(23\pm4\pm2)\%$
for the B meson. The first error comes from the sum rule uncertainty, the
second one from unknown or not accurately known matrix elements in HQET. We
obtain a ratio of vector to pseudoscalar decay constant of
$1.00\pm0.07+O(1/m_Q^2)$ for B mesons.
