This paper presents the results of the first statistical study of interplanetary directional discontinuities at both low and high heliographic latitudes measured by the Ulysses magnetometer. There is a gradual decrease in the rate of occurrence of interplanetary discontinuities (ROIDs) with increasing radial distance. From 1 to 5 AU, an e-(r-1)/5 dependence is derived. Much of this decrease is believed to be an artifact due to the discontinuity thickening with decreasing |B|, falling outside the detection criteria. As Ulysses goes from the ecliptic plane to high (-80¿) heliographic latitudes, the ROID value increases dramatically. The increase is about a factor of 5 as Ulysses moves from Jupiter at 5 AU to 2.5 AU over the south pole. There is a one-to-one correspondence between high ROID values and high-speed streams. This is particularly dramatic just after the Jovian encounter when there are ~25.4-day period corotating streams present. Thus the increase with latitude is primarily due to Ulysses spending an increasing percentage of time within a high-speed stream emanating from the solar coronal hole. High-speed streams are characterized by the presence of nonlinear Alfv¿n waves with peak-to-peak transverse fluctuations as large as |ΔB↘|/|B| of 1 to 2. Over the south pole, the normalized transverse wave power can be characterized by P=2.5¿10-4f-1.6 Hz-1 and the compressional power 1.8¿10-4f-1.2 Hz-1 for frequencies between 10-5 and 10-2 Hz. The normalized wave power spectra in different regions of the polar coronal hole streams, from midlatitudes to high heliographic latitudes, appear to be quite similar. The wave power in the ecliptic plane is somewhat lower, perhaps due to contamination from low-speed streams. The Alfv¿n waves in the high-speed stream are found to be propagating outward from the Sun, even at these large heliocentric distances (2.5--5.0 AU). The waves typically have arclike polarizations and conserve field magnitude to first order. Directional (rotational) discontinuities often from the edges of the phase-steepened Alfv¿n waves, thus offering a natural explanation for the high ROID rates within high-speed streams. ¿ American Geophysical Union 1996