In this paper the spectral distribution of turbulent energy is considered. The turbulence is assumed to be homogeneous and axisymmetric with a vertically directed axis of symmetry.The spectral representation of the velocity correlation equation was the starting point for determining the spectra of turbulent energy. Transfer of energy in axisymmetric turbulence was approximated by adopting a Heisenberg-type hypothesis. The general solution obtained presents as special cases the −5/3 law and the −11/5 law for the spectrum of total energy.It is shown that the spectrum of the vertical energy behaves like k−5/3 for large wave numbers and like k−5/3 for buoyancy subrange. The spectrum of temperature fluctuations is also investigated.