Dissipative multi-pulse three-wave coupled states, appearing with collinear Bragg light scattering in a two-mode square-law nonlinear medium with linear non-optical losses, are revealed. Both the localization conditions and the spatio-temporal distributions of their optical components are studied theoretically in quasi-stationary and non-stationary regimes. Then, dissipative multi-pulse three-wave coupled states have been observed within the acousto-optical experiments in a calcium molybdate crystalline collinear cell. The obtained experimental results are in rather good agreement with the non-stationary theory developed.