We present the results of initial experiments on the coarsening of coherent precipitates of the gamma phase (Ni-Al solid solution) in a matrix of off-stoichiometric gamma' (Ni3Al). The compositions of the gamma' phase were 22.25, 22.33 and 22.6 at. % Al. The alloys-were aged at 650 degreesC. The volume fractions of the gamma precipitates, f(gamma), were calculated to be 0.053, 0.046 and 0.023, respectively. The longest aging times exceeded 750 h. Precipitates of the gamma phase are spherical when very small, but become cuboidal at small sizes (<7 nm), with interfaces parallel to {100}. They also coalesce readily because there are no antiphase relationships among nearest neighbors, unlike the situation for gamma' precipitates in a gamma matrix. The gamma precipitates are thus highly non-equiaxed at relatively small sizes compared to gamma' particles. At short aging times the data obey the classical rate law for diffusion-controlled coarsening, (3) approximate to kt, where is the average radius at time t and k is the rate constant. For these data k increases with increasing f(gamma). However, if the data on all aging times are included in the analysis the rate law is not nearly so well obeyed, but the values of k are nearly independent of f(gamma). The correct dependence of k on f(gamma) requires additional experiments for resolution.