  We extend the calculations of the spin alignments of vector mesons in
$e^+e^-$ annihilation in a recent Rapid Communication to deeply inelastic
lepton-nucleon scatterings. We present the results for different mesons in the
current fragmentation regions of $\mu^- N$$ \to$$ \mu^- VX$ at high energies
and $\nu_\mu N $$\to$$ \mu^- VX$ at both high and low energies. We also present
the predictions for $\nu_\mu N$$ \to$$ \mu^- VX$ at NOMAD energies in the
target fragmentation region using a valence quark model.
