Double and multiple irreducible products of irreducible tensor operators O^(ki)(J) obeying special commutation relations arising from the properties of angular momentum operators are considered. It is shown that the double product can be expressed in terms of another set O^(k) associated with a coupling coefficient epsilon _k^(k1,k2) defined by (O^(k1)*O^(k2))^(k)= epsilon _k^(k1,k2)O^(k). An analytical expression has been derived for the coupling coefficient epsilon _k^(k1,K2) and its values are tabulated for k₁ and k₂ up to 3. It is proved that (O^(k1)*O^(k2))^(k)=(O^(k2)*O^(k1))^(k). Multiple irreducible products are also discussed. The coupling coefficients for triple products are tabulated for Sigma _ik_i up to 6. Some important special cases of quadruple products are dealt with explicitly. Applications of the present results to high-order effects in spectroscopy are investigated.