Statistical heterogeneity of abyssal hill properties is often evident in seafloor topography, even under periods of relatively constant spreading direction and rate. In this paper we relate the statistics of topographic slopes computed on finite spatial scales to the autocovariance function and investigate the practicality of using these functions in describing such heterogeneous abyssal hill terrains. For a two-dimensional homogeneous surface, a direct relation exists between the sample autocovariance and the slope distributions at different spatial scales. However, for a heterogeneous field characterized by large transient signals, the computed autocovariance estimate no longer has a clear statistical interpretation and becomes dominated by the transients. In contrast, the family of slope distributions can still be used to derive stable descriptors of the field. Slope statistics are thus useful in deriving a more robust estimate of the autocovariance than the usual sample autocovariance. Moreover, slope statistics may also be used to derive stable estimates of quantities not measurable with the autocovariance function or power spectra, such as the statistical asymmetry of features. Examples of the use of slope statistics and a comparison with autocovariance methods are presented. We document and quantify evidence of statistical asymmetry in a region of abyssal hills in the northeast Pacific and, in a second example, the presence of multiple lineations in a region where a fracture zone cuts through abyssal hill terrain. ¿ American Geophysical Union 1990