  In this paper, we provide a uniform method to thoroughly classify all
Harish-Chandra modules over some Lie algebras related to the Virasoro algebras.
We first classify such modules over the Lie algebra $W(\varrho)[s]$ for
$s=0,\frac12$. With this result and method, we can also do such works for some
Lie algebras and superconformal algebras related to the Virasoro algebra,
including the several kinds of Schr\"odinger-Virasoro Lie algebras, which are
open up to now.
