  Let ${\mathcal A}$ be a generalized $q$-Weyl algebra, it is generated by $u$,
$v$, $Z$, $Z^{-1}$ with relations $ZuZ^{-1}=q^2u$, $ZvZ^{-1}=q^{-2}v$,
$uv=P\big(q^{-1}Z\big)$, $vu=P(qZ)$, where $P$ is a Laurent polynomial. A
Hermitian form $(\cdot,\cdot)$ on ${\mathcal A}$ is called invariant if
$(Za,b)=\big(a,bZ^{-1}\big)$, $(ua,b)=(a,sbv)$, $(va,b)=\big(a,s^{-1}bu\big)$
for some $s\in {\mathbb C}$ with $|s|=1$ and all $a,b\in {\mathcal A}$. In this
paper we classify positive definite invariant Hermitian forms on generalized
$q$-Weyl algebras.
