Baroclinically unstable Eady waves representing solutions of a two-dimensional, uniform potential vorticity, semigeostrophic model are considered. These semigeostrophic waves are expressed as linear solutions in geostrophic coordinate space (X,Z,T), but they satisfy a nonlinear advection equation in physical space (x,z,t). The transformation of the velocityv(X,Z,T) into a physical space solutionv(x,z,t) is accomplished by an approximate technique that represents a truncation at second-order in the Rossby number. Two nonlinear processes are delineated: there is nonlinearity inherent in the transformation (X,Z,T)→(x,z,t), and there are nonlinear interactions between the waves. Solutions, representing the interaction of two semigeostrophic waves, are determined for initial conditions that span a range of wave-numbers. Under these conditions both single and double frontal structures (one or two concentrated cyclonic shear zones) can develop. The most significant nonlinear interactions between the unstable waves are primarily associated with these concentrated regions of cyclonic shear, and the magnitude of the shear may either be enhanced or diminished by the interacting wave disturbances. The unstable growth rate may vary with time and, in all cases examinedv(x,z,t) develops an infinite slope in a finite timetc. It is shown that two interacting semigeostrophic waves are characterized by a minus eight-third power law spectrum at timetc, a result previously established by Andrews and Hoskins (1978) for one wave. The present results are not significantly altered by the inclusion of an Ekman layer, in which the unstable waves propagate at different phase speeds.