The relative position and relative proper motion of the radio sources 3C 345 and NRAO 512 were estimated from four sets of very-long-baseline interferometric observations, spaced between October 1971 and May 1974. Use of phase-connection techniques yielded the result ..cap alpha.. (3C345-NRAO 512) =2/sup m/ 29/sup s/.436 68 +- 0/sup s/.000 03 delta (3C345-NRAO 512) =1' 40''.726 3 +- 0''.000 3 for the separation in 1950.0 coordinates of the centers of brightness of the compact components of the two sources, and an upper bound of 0''.000 5 per year on their relative proper motion (70% estimated confidence limits).