We study unsteady Gortler vortices excited by free-stream vortical disturbances (FSVD) in compressible boundary layers. The receptivity mechanism in the linear regime has been recently studied by Viaro and Pierre (2019), who showed that compressible Gortler vortices are effectively induced by small-amplitude FSVD. In the present study, the focus is instead on the nonlinear development of compressible Gortler vortices exposed to elevated FSVD. The free-stream Mach number is an order-one quantity. The formation and evolution of the Gortler flow are governed by the compressible nonlinear boundary-region equations, supplemented by appropriate initial and boundary conditions which characterise the impact of the FSVD on the boundary layer. The curvature effect was studied for Gortler vortices excited by FSVD at Tu = 2% and Mach number 0.69, which refers to typical experimental conditions of turbomachinery applications (Arts, 1990). It is found that low-frequency, i.e. long-wavelength, components of the FSVD are the primary factor in the generation of the Gortler vortices. Although the FSVD consists of vortical disturbances, thermal fluctuations are excited in the boundary layer because of the momentum-energy coupling caused by compressibility. Figure 1 (a) shows the downstream development of the maximum r.m.s. of the streamwise velocity. The concave wall (positive G) is found to destabilise the flow, whereas the convex wall (negative G) has a stabilizing effect. The Blasius base flow is highly distorted by the excited vortices, especially at the outer edge of the boundary layer. Figure 1 (b) shows the nonlinear structure of Gortler vortices excited by the elevated FSVD.