  This paper deals with the 2-D Schr\"odinger equation with time-oscillating
exponential nonlinearity $i\partial_t u+\Delta u= \theta(\omega
t)\big(e^{4\pi|u|^2}-1\big)$, where $\theta$ is a periodic $C^1$-function. We
prove that for a class of initial data $u_0 \in H^1(\mathbb{R}^2)$, the
solution $u_{\omega}$ converges, as $|\omega|$ tends to infinity to the
solution $U$ of the limiting equation $i\partial_t U+\Delta U=
I(\theta)\big(e^{4\pi|U|^2}-1\big)$ with the same initial data, where
$I(\theta)$ is the average of $\theta$.
