Osmotic coefficients of aqueous solutions of 3,3-, 4,5-, 6,6-, and 6,9-ionenes with bromide and chloride counterions were measured at 298 K and in the concentration range from 0.001 to 0.1 mol/dm(3). The measured osmotic coefficients are very low, indicating large deviations from ideality caused by strong interactions in these systems. The solutions with chloride counterions have a higher osmotic coefficient than the corresponding bromide solutions, which is in agreement with experimental data for the counterion activity coefficient of these solutions. The experimental results for osmotic coefficients were analyzed using a cylindrical cell model where a fixed charge is assumed to be uniformly distributed along the z-axis of a rigid and impenetrable polyion, in conjunction with the classical Poisson-Boltzmann equation. More refined models in which discrete charges are located periodically along the z-axis of the polyion were also studied. In the latter case the canonical Monte Carlo method was used to calculate the osmotic coefficient. In agreement with previous studies of weak and moderately charged polyelectrolytes, we found the theoretically predicted osmotic coefficients to be too high in comparison with the experimental data for aqueous ionene solutions.