  Let $(X, T^{1,0}X)$ be a compact connected orientable strongly pseudoconvex
CR manifold of dimension $2n+1$, $n\geq1$. Assume that $X$ admits a connected
compact Lie group $G$ action and a transversal CR $S^1$ action, we compute the
coefficients of the first two lower order terms of the equivariant Szeg\H{o}
kernel asymptotic expansions with respect to the $S^1$ action.
