PKP(BC) versus PKP(DF) differential travel times show coherent patterns of residuals indicating aspherical structure within the Earth's inner core. Using a waveform correlation method, we measure 318 differential PKP(BC) versus PKP(DF) travel times from 5 years of Global Digital Seismograph Network (GDSN) short-period data at ranges between 145¿ and 155¿. In addition, we obtain 19,470 probable BC versus DF travel times at these ranges by searching through 23 years of the International Seismological Centre (ISC) catalog. Plots of residuals versus turning point location and residuals versus ray direction show clear patterns which indicate that the differential travel times are highly correlated along similar ray paths. This pattern is robust with respect to range and source depth. These anomalies are almost certainly due to aspherical inner-core structure since PKP(BC) and PKP(DF) have nearly coincident ray paths in the mantle and outer core. The GDSN and ISC residual patterns are in general agreement, but the ISC residuals underpredict the GDSN residuals by about a factor of 2. The ISC data have better spatial coverage, particularly for N-S ray paths within the inner core. These N-S ray paths show positive residuals of about 0.5 s, indicating faster inner-core P velocities in this diretion, a result consistent with previous studies of absolute PKP(DF) travel times but derived from an independent data set. Due to the sparse ray coverage of our data, either heterogeneity or anisotropy within the inner core with about 1% velocity variations could explain these residual patterns. However, inversions of the ISC data for heterogeneity require many more free parameters to achieve the same variance reduction as a simple two-parameter anisotropy model. ¿1991 American Geophysical Union