The structure of the heliospheric current sheet (HCS) at Ulysses and at Wind is compared during the period of near-radial alignment in 1998. Electron heat flux and magnetic field data are used to determine true magnetic field polarity. During the solar rotation period surrounding alignment there was considerable disagreement between the HCS crossings at Wind and those predicted from the corresponding source surface map, both in number and in location, consistent with the disordered, temporally varying solar wind at this ascending phase of the solar cycle. Despite this complexity the four crossings closest to the time of radial alignment at Wind were successfully identified in Ulysses data with use of a one-dimensional hydrodynamic code. Further, minimum variance analysis for the first two crossings, which were separated by only 16 hours at Wind, indicated coherent propagation of a large-scale warp in the HCS. Analysis of the local structure of the HCS on the four crossings, however, revealed a high level of variability both from case to case and from one spacecraft to the other. For example, the third crossing at Wind was a single-sheet crossing adjacent to structures with fields folded back on themselves and a brief period of counterstreaming electrons implying a transient structure. At Ulysses multiple sheets were encountered. At the fourth crossing Wind passed through a counterstreaming event with a flux rope signature containing a south pointing axis, while Ulysses passed through a flux tube with little field rotation and northward pointing field. The results are consistent with the view that the heliospheric current sheet is coherent as a global structure but highly variable in local structure over angular distances of a few degrees.