We have used sidereal dirunal variations observed by neutron monitors and surface and underground muon telescopes to examine the north-south anisotropy and radial density gradient of high-energy galactic cosmic rays between 1957 and 1985. We have derived the average amplitude and rigidity spectrum of the anisotropy for this period and estimate the radial gradient to be best represented as a function of rigidity P by 1.02¿(P/10)-0.5 % AU-1 for rigidities less than ≈450 GV. The temporal variation of both the north-south anisotropy and the radial density gradient show a solar cycle variation. Possible dependence of the anisotropy on the solar magnetic polarity state has been examined under the assumptions of a static and a nonstatic rigidity spectrum, with conflicting results. We show that the analysis is affected by a further sidereal varation and that the responsible anisotropy is related to the asymmetric heliospheric modulation of a galactic anisotropy. ¿ American Geophysical Union 1994