The detailed description of the product operator formalism for a weakly coupled IS (I = 1/2, S = 3/2) spin system has been presented and the shorthand notations for the evolutions of I-x, I-y, IxSz and IySz product operators under the spin-spin coupling Hamiltonian have been obtained in a different form. Furthermore, as an application and a verification, the product operator formalism has been used for the analytical description of a 2D J-resolved nuclear magnetic resonance (NMR) experiment for IS (I = 1/2, S = 3/2) spin systems. (C) 2002 Elsevier Science B.V. All rights reserved.