The M 1 and E 2 reduced transition probabilities in 191Ir and 199Ir have been calculated on the weak particle-core coupling model. The static moments of the ground state and the first three low-lying excited states have been computed. The theoretical values are in good agreement with the experimental results, in particular, the existing discrepancy between the theoretical and the experimental value for the magnetic moment of the first excited 5/2 + state, in both these nuclei, has been removed. The predicted sign of the quadrupole moment of the 2 + state in the neighbouring even-even nuclei is consistent with the results reported for Platinum nuclei. The level structure of both these nuclei has been calculated assuming the particle-core interaction to be dipole-dipole and quadrupole-quadrupole type.