A time-domain model that describes wide-angle paraxial propagation of acoustic pulses in shallow water is developed. This model incorporates weak nonlinear effects and depth variability in both ambient density and sound speed. Derivations of paraxial approximations are based on an iterative approach, in which the wide-angle approximation is obtained by using a narrow-angle equation to approximate the second range derivative in the two-way equation. Scaling arguments are used to obtain a more tractable simplification of the equation. The wide-angle equation is solved numerically by splitting into components representing distinct physical processes and using a modified version of the time-domain parabolic equation (TDPE) code [M. D. Collins, J. Acoust. Soc. Am.84, 2114–2125 (1988)]. A high-order upwind flux-correction method is modified to handle the nonlinear component. Numerical results are presented for adiabatic propagation in a shallow, isospeed channel. It is demonstrated that nonlinear effects are significant, even at small ranges, if the peak source pressure is high enough. Both nonlinear and wide-angle effects are illustrated, and their differences are discussed.