Energy spectrum equations for homogeneous axisymmetric turbulence are formulated using the eddy‐damped quasinormal Markovian (EDQNM) approximation. The equations, which consist of two spectrum functions of the two variablesk(the magnitude of the wavevectork) and &mgr; (the cosine of the angle betweenkand the direction of axisymmetry), are computed directly, without any reduction, under initial conditions for different degrees of anisotropy. In this paper, the results for cases of medium anisotropic and nearly two‐dimensional initial conditions are reported. A remarkable result was that in the nearly two‐dimensional case, some characteristic properties of two‐dimensional isotropic turbulence, such as inverse energy cascades, are observed. Also, particular attention is paid to the effects of pressure‐strain correlation and inertial energy transfer on the return of anisotropic turbulence to isotropy.