  We consider a neutrino source at rest and discuss a condition for the
existence of neutrino oscillations which derives from the finite lifetime
$\tau_S$ of the neutrino source particle. This condition is present if the
neutrino source is a free particle such that its wave function is
non-stationary. For a Gaussian wave function and with some simplifying
assumptions, we study the modification of the usual oscillation probability
stemming from $\tau_S$. In the present accelerator experiments the effect of
$\tau_S$ can be neglected. We discuss some experimental situations where the
source lifetime becomes relevant in the oscillation formula.
