By measuring the frequency dispersion of time-gated radar echoes from Venus and Mercury at the Arecibo Ionospheric Observatory, the apparent rotation rates of these planets have been unambiguously determined. The combination of many such measurements made over a period of time has permitted a separation of the intrinsic rotation from the contribution of the relative orbital motion of the earth and the target planet. From observations over a three-month period surrounding the inferior conjunction of 1964, we find that Venus has a solar rotation period (i.e., with respect to the planet-sun line) of 117+1 days and a sidereal rotation period of 245.1+2 days (retrograde); its rotation axis has a declination of -66.7+1 deg and a right ascension of 90.3+1 deg (1950.0). The inclination of the axis is -89.8+1 deg with respect to the ecliptic and -86.7+1 deg with respect to the orbital plane of Venus. These results are consistent with Venus making four complete axial rotations as seen by an earth-based observer between inferior conjunctions. For such a retrograde rotation a sidereal period of 243.16 days is required. Data obtained near the inferior conjunctions of Mercury in April and August 1965 indicate that the axial rotation of Mercury is direct and has an average solar period of 176+9 days and a sidereal period of 59+3 days. The direction of the rotation axis, although not well determined by these data, seems to be inclined to the normal to Mercury's orbital plane by less than 280. These results are consistent with Mercury's axial rotation being locked to its orbital motion such that the sidereal period of the former is exactly two-thirds of that of the latter. Enhanced scattering from distinct parts of the Venus surface have also been detected and a corresponding contour map of the surface radar reflectivity is presented.