We present large-eddy simulations of the turbulent compressible flow at a low Mach number in curved ducts. The aim is to investigate the influence of the curvature radius Rc on the flow. Three simulations are carried out at Rc = 3.5 Dh, 6.5 Dh and 10.5 Dh (Dh hydraulic diameter). We first validate our computations by comparison with the incompressible experiments performed by Chang et al. (1983). We observe that the decrease of the curvature radius is accompanied by a strong intensification of the secondary transverse flows : a rise of 100% of the maximum of their intensity is obtained between the smaller and the higher values of Rc. We show that the secondary flows strength is directly related to the radial pressure gradient intensity. We observe a significant modification of the near-wall laws in the vicinity of each curved walls in correlation with the favourable or the adverse streamwise pressure gradient depending on the nature of the curvature. The influence of Rc on the coherent vortices is also estimated.