In this article, we consider the Cauchy problem for dispersive equations in $\alpha$-Modulation spaces. For this purpose, we find a method for estimating $u^k$ in alpha-modulation spaces when k is not an integer, and develop a Strichartz estimate in $M_{p,q}^{s,\alpha}$ which is based on semigroup estimates. In the local case, we that the domain of p is independent of $\alpha$, which is also the case in the Modulation spaces and in the Besov space.