It is proposed that acoustic nuclear magnetic resonance be used to detect steady‐state nuclear orientation achieved by the Jeffries Abragam effect. This is a new scheme for double magnetic resonance (ADMR) in contrast with conventional DMR, which employs the usual time‐varying magnetic field to observe the enhancement of the nuclear resonance. The acoustic wave modulates the nuclear quadrupole interaction to induce double as well as single spin flips. Calculations for nuclei of spinI = 32in weak dipolar coupling with paramagnetic electrons of spinS = 12in an axial crystal indicate that both types of DMR should give positive and negative enhancements ∼gβ /gnβn∼103for 1° ⩽T⩽ 300°K in favorable circumstances. Suitable samples in which the effect might be demonstrated are iodine nuclei in NaI containingI2−centers and27Alnuclei inCr3+orV3+dopedAl2O3. If the related experiments are performed, the effect of the electron paramagnetic resonance linewidth and of nuclear‐spin diffusion may well reduce the enhancement by one or two orders of magnitude.