We propose a theta1-t1-theta2 pulse-NMR experiment to detect the spin-diffusion anisotropy, Delta=Dpar-Dbottom, in degenerate spin-polarized3He-4He mixtures, where Dbottom and dparare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the 3He concentration x3 ap 4% the spinrotation parameter vanishes (mgrM rarr0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of DeltaD. For slight anisotropy, i.e. DeltaD/Dpar lap0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small mgr M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for DeltaD/Dpar = 0.5 the heights are ap 2 % of the first echo, and should be detectable. The (theta1, theta2) tip-angle dependence of the DeltaD echoes is different from that of the mgrM and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the theta1-t1-theta2 experiment provides a sensitive means of detecting the anisotropy.