The general analytical solution of a collisional‐radiative model, including atom–atom inelastic collisions, for nonequilibrium, partially ionized, steady‐state plasmas is presented. This is applied to argon plasmas and the results are compared with previous numerical calculations. The model includes three atomic energy levels; the ground level, one excited level, and continuum, and assumes a Maxwellian electron and atom distribution functions. All rates for collisional and radiative processes are expressed as analytical functions. The model is solved algebraically to obtain analytical expressions for the electron and excited atom densities as a function of the plasma parameters. In the limit of an optically thick plasma the solution agrees with results for complete thermodynamic equilibrium. Solutions are presented for a wide range of conditions (3000≤Te≤24 000 K, 105≤Ne≤NAcm−3, 1014≤NA≤1018cm−3).