  We prove that any irreducible Harish-Chandra modules for a class of Lie
algebras, which we call gap-$p$ Virasoro algebras, must be a highest weight
module, a lowest weight module, or a module of intermediate series.These
algebras are closely related to the Heisenberg-Virasoro algebra and the algebra
of derivations over a quantum torus. They also contain subalgebras which are
isomorphic to the Virasoro algebra $Vir$, but graded by $p\mathbb Z$(unlike
$Vir$ by $\mathbb Z$).
