In this paper we consider the regularity of solutions to nomlinear Schrödinger equations (NLS),
[
\begin{aligned}
i \hat{C}, u+\frac{1}{3} | u & =F(u, u) . & & (t, x) \in \mathbb{R} \times \mathbb{B}^{\prime \prime}, \
u(0) & =\phi . & & x \in \mathbb{R}^{u} .
\end{aligned}
]
where (F) is a polynomial of degree (p) with complex coefficients. We prove that if the initial function (\phi) is in some Gevrey class, then there exists a positive constant (T) such that the solution (u) of NLS is in the Gevrey class of the same order as in the initial data in time variable (t \in[-T, T] \backslash 0). In particilar, we show that if the initial function (\phi) has an analytic continuation on the complex domain (\Gamma_{1, f}=) (i=\in \mathbb{C}^{\prime}: z_{1}=x,+i y_{1}, \quad-x0 ;) (see Fig. 1), where (0<x=\sin { }^{\prime} A_{1}<\pi 2) and (0<A_{1}<1), then there exists positive constants (T) and (\beta) such that the solution (u) of NLS is analytic in time variable (t \in[-T, T] \backslash 0) and has an analytic continuation on (:=1=1+i \tau); jarg (\left.z_{11}<\beta<\pi 2 . \quad \mid t i<T\right}). where (\sin \beta<\operatorname{Min}\left{\sqrt{2} A_{1}\left(1+\sqrt{2} A_{1}\right), 2 A_{2}\left(3 A_{2}+\right.\right.) (\sqrt{2 e}(1+R)); when (|x|<R . \quad) " 1995 Academic Press. Inc.