  We discuss the production of hadrons in $e^+e^-$ collisions at $\sqrt s=91$
GeV. We address the question wether the particle yields measured in the final
states are consistent with the statistical model predictions. In the model
formulation we account for exact conservation of all relevant quantum numbers
using the canonical description of the partition function. Within our model the
validity of the thermodynamical approach to quantify particle production in
$e^+e^-$ annihilations is not obvious.
