The introduction of the cross-polarization technique made it possible to overcome the low sensitivity of dilute spins, and provided a means of observing the NMR signals of those nuclei in solids (I). However, this method cannot readily be applied to nuclei with low gyromagnetic ratios, such as, 57Fe, ‘03Rh, ‘*‘OS, etc., because to achieve the Hartmann-Hahn condition (2) with those nuclei, very high values of the rf power are required. Recently, Bax et al. (3) have proposed an interesting new technique utilizing off-resonance effects (4) which effectively reduce the rf power requirements for crosspolarization. While Bax et al. demonstrated the successful application of their method for a static sample of 15N-enriched glycine, they noted that there are several difficulties with their technique. In that method, rf inhomogeneity can easily cause a mismatch of the Hartmann-Hahn condition, and the technique is experimentally difficult to apply. Another method of cross-polarization using multiple-pulse irradiation on the Z spins has been proposed by Quiroga and Virlet (5). In this method, an HW-8 multipulse sequence (6) was employed to perform two conflicting demands at the same time: (i) to suppress the homonuclear dipolar interaction, and (ii) to provide a spin-locking field for the Z spins. Since a perfectly tuned WAHUHA-4 (7) type homonucleardecoupling pulse sequence cannot provide the Z spin-locking field, one has to introduce the pulse length “error” into the pulse sequence without destroying the homonucleardecoupling effect. Therefore, in the Quiroga and Virlet method, it is difficult to control the Z spin-locking field strength provided by the pulse length “error.” We present an alternative method to reduce the rf power requirements for the cross-polarization of nuclei with small gyromagnetic ratios, which we find to be easy to apply, and which is based on the time average of the precession frequency. Recently, we have shown that by alternating the phase of the Z spin-locking rf field, the precession of an Z spin isochromat around the effective field is time reversed (8). In a tilted rotating frame, the time-evolution operator describing the overall precession of the Z spin isochromat around the effective field after a one cycle time tc = t, + t2 of the phase-alternating spin-locking pulse sequence (Fig. 1) can be written as