In this dissertation, we investigate the well-posedness and persistence of spatial analyticity of the solution for nonlinear evolution dispersive higher order KdVBBM-type equations which governs waves on shallow water surfaces. We considered the initial value problem (IVP) associated with a fth order KdV-BBM type model that describes the propagation of the unidirectional water wave. We show that the uniform radius of spatial analyticity (t) of solution at time t cannot decay faster than 1=t for large t > 0, given initial data that is analytic with xed radius . This signi cantly improve the previous result an exponential decay rate of (t) for large t obtained in [28]. 0 We also considered the initial value problem (IVP) associated with generalized KdV-BBM equation and coupled system of generalized BBM equations, subject to initial data which is analytic in modi ed Gevrey space with a xed radius . It is shown that the uniform radius of spatial analyticity of solutions for both problems can not decay faster than ct 2=3 as t ! 1. We proved the global well-posedness result of Kadomtsev, Petviashvili - Ben- jamin, Bona, Mahony (KP-BBM II) equation in an anisotropic Gevrey space, which complements earlier results on the well-posedness of this equation in anisotropic Sobolev spaces. In addition, we analyzed the evolution of the radius of spatial analyticity of the solution and we obtained asymptotic lower bound for the radius of spatial analyticity of the solution for the KP-BBM II equation. We used the conservation law, contraction mapping principle and di erent multilinear estimates to obtain the results.