  We discuss the rigidity of elliptic genera for non-spin manifolds $M$ with
$S^1$-action. We show that if the universal covering of $M$ is spin, then the
universal elliptic genus of $M$ is rigid. Moreover, we show that there is no
condition which only depends on $\pi_2(M)$ that guarantees the rigidity in the
case that the universal covering of $M$ is non-spin.
