The theory of rotary resonance in multiple-quantum magic-angle spinning (MQMAS) experiment is presented. The rotary resonance effect can enhance the efficiency of MQMAS experiment for high-resolution NMR spectra of half-integer quadrupolar nuclei [J. Chem. Phys. 114 (2001) 4618]. Using a spin-1/2 formalism and Floquet theorem, the spin dynamics of a spin-3/2 under rf irradiation and magic-angle sample spinning is solved analytically in a doubly rotating frame. The results show an oscillatory behavior of MQ excitation with nulls at omega(1) = nomega(r)/2, where omega(1) represents the rf field strength and omega(r) is the spinning frequency. Efficient MQ excitation occurs between these nulls and MQ conversion peaks at omega(1) = nomega(r). The origin of the rotary resonance phenomenon is related to frequency shift of a general two-level system under a randomly modulated periodic perturbation. (C) 2002 Elsevier Science B.V. All rights reserved.