A strong external dc magnetic field introduces a basic anisotropy into incompressible magnetohydrodynamic turbulence. The modifications that this is likely to produce in the properties of the turbulence are explored for the high Reynolds number case. The conclusion is reached that the turbulent spectrum splits into two parts: an essentially two‐dimensional spectrum with both the velocity field and magnetic fluctuations perpendicular to the dc magnetic field, and a generally weaker and more nearly isotropic spectrum of Alfve´n waves. A minimal characterization of the spectral density tensors is given. Similarities to measurements from the Culham–Harwell Zeta pinch device and the University of California, Los Angeles Macrotor tokamak are remarked upon, as are certain implications for the Belcher and Davis measurements of magnetohydrodynamic turbulence in the solar wind.