The oscillation continuum in laser-induced fluorescence spectra of bound-free c 3 Σ + → a 3 Σ + and (4) 1 Σ + → X 1 Σ + transitions of the KCs molecule were recorded by Fourier-transform spectrometer and modelled under the adiabatic approximation. The required interatomic potentials for ground a 3 Σ + and X 1 Σ + states were reconstructed in an analytical Chebishev-polynomial-expansion form in the framework of the regularization direct-potential-fit procedure based on the simultaneous consideration of experimental line positions from [R. Ferber et al, Phys. Rev. A, 80, 062501 ( 2009)] and the present ab initio calculation of short-range repulsive potential data. It was proved that the repulsive part over dissociation limit of the derived a 3 Σ + potential reproduces the experiment better than the potentials reported in literature. It is also shown that all empirical and semi-empirical potentials available for the X 1 Σ + state reproduce the bound-free (4) 1 Σ + → X 1 Σ + spectrum with equal quality in the range of observations.