We describe a new scheme for computing the asymmetric part of the cosmic ray particle density gradient. The method makes use of the ecliptic components (Ar,Aϕ) of the cosmic ray solar diurnal anisotropy observed with a detector on spinning Earth and the interplanetary magnetic field sector structure in the heliosphere. We apply this methodology, to compute the magnitudes and directions of the asymmetric (G&thgr;a) particle density gradient in the heliosphere for selected intervals of time during the 1965 to 1993 period. Data from six detectors of the global network are used for this purpose. Their median rigidity of response (Rm) covers the following range: 10 GV≤Rm≤300 GV of the galactic cosmic ray (GCR) spectrum. We find that G&thgr;a is well behaved over an intermediate rigidity range (10 GV≤Rm≤67 GV) where it is inversely proportional to the rigidity (R) of the GCR protons. At higher rigidities (R≥100 GV), it may fall off more steeply and even reverse sign at large (≳1 AU) off-ecliptic distances. The direction of G&thgr;a changes consistently immediately after each observed solar polar field reversal. Sudden, conspicuous, short-lived (~1 year) reversals of G&thgr;a are observed during the declining phases of solar activity cycles 20 (1974) and 21 (1984). They may be caused by a sudden burst of solar activity late in the cycle. We have determined G&thgr;a values from Deep River neutron monitor data (Rm=16 GV) for the 1965 to 1993 period. Extreme computed values range from (3.0¿0.8)%/AU in 1968 to (-2.4¿0.8)%/AU in 1987.¿ 1997 American Geophysical Union