We first introduce the analytical descriptions of INEPT (insensitive nuclei enhanced by polarization transfer) nuclear magnetic resonance experiment for weakly coupled IS (I = 1/2, S = 5/2) spin systems by using the product operator formalism. The results calculated for the intensities and positions of the observable signals are simulated for the molecules containing {Al-27 (S = 5/2), Si-29 (I = 1/2)} and {Al-27, P-31 (I = 1/2)} nuclei by using the Maple program. The simulated spectra were in very good agreement with the experimental spectra of INEPT experiments for the microline and TMP-AlCl3 complex in NaX zeolite under magic angle spinning conditions. Futhermore, in order to complete the calculations we also present the analytical descriptions of the INEPT sequence for weakly coupled IS2 and IS3 spin systems.