  We determine several necessary and sufficient conditions for a closed
almost-complex orbifold $Q$ with cyclic local groups to admit a nonvanishing
vector field. These conditions are stated separately in terms of the orbifold
Euler-Satake characteristics of $Q$ and its sectors, the Euler characteristics
of the underlying topological spaces of $Q$ and its sectors, and in terms of
the orbifold Euler class $e_{orb}(Q)$ in Chen-Ruan orbifold cohomology
$H_{orb}^\ast (Q; \R)$.
