Interplanetary discontinuities have been investigated at heliocentric distances between 1 and 8.5 AU by using Pioneer 10 and 11 vector helium magnetometer observations. The principal purpose of the study was to investigate a possible dependence of the rate of occurrence and properties of the discontinuities on radial distance. This objective required a separation of spatial and temporal variations and used the simultaneous nearly continuous data from both spacecraft. Discontinuities were identified by using carefully developed criteria that were shown to be comparable to those used in earlier studies but which are still applicable in the weak magnetic fields that are typical of large radial distances. Special attention was given to the identification of relatively thick discontinuities in the expectation that discontinuities might grow progressively thicker with distance. The statistics associated with the rate of occurrence of discontinuities have been shown to be well approximated by a Poisson distribution. The rate of occurrence of discontinuities undergoes large variations, from day to day and from one solar rotation to another, which are well outside the deviations to be expected on the basis of statistical fluctuations alone. Temporal changes in the rate of occurrence averaged over Bartels solar rotations were well correlated at Pioneer 10 and 11, which were separated by a distance of ?2 AU. The time variations consisted of a slow modulation of the rate of occurrence such that successive increases and decreases persisted for several months at a time, presumably as a result of changing solar conditions. The correlation over widely separated distances is most simply interpreted by a model in which the discontinuities originate inside 1 AU, probably near the sun, and are convected outward by the solar wind. Further support for this model is provided by the statistical properties of the discontinuities at 1 and 5 AU, which were found to be very similar. Clear evidence of a decrease in the rate of occurrence p with distance has been obtained. The simultaneous rates from the two spacecraft reveal that this decrease is well approximated on the average by the function p=50e-R-1/4 and imply a radial gradient of 25% per astronomical unit. This gradient may be apparent and does not necessarily imply that discontinuities actually occur less frequently at large radial distances. The decreased rate of occurrence may be associated with an increasing thickness of the discontinuities such that they no longer satisfy the identification criteria. Possible evidence of a dependence of p on heliographic latitude was sought, but no statistically significant dependence was found. The results of this study are inconsistent with previous inferences of a very large radial or latitudinal gradient on the basis of Pioneer 8 data (Mariani et al., 1973). The reason for this earlier result was probably the influence of time variations which occurred on a scale of several months, as was found in our study, and masqueraded as spatial variations.