Observations of 64-64-arcsec and 65 x 65-arcsec regions around 21 nearby stars, obtained with UKIRT and AAT, respectively, in March and June, 1981, are reported. The survey was undertaken to search for 'black dwarf' (0.001-0.08-solar-mass, 0.1-solar radius) companion objects. The limiting K magnitudes for the telescopes were about 14.5 and 15.0, and all objects detected were measured at J, H, and K to calculate approximate temperatures and radii. Black-dwarf candidates were defined as objects with temperatures less than about 2500 K and radii about 0.2 solar radius, but no such objects were found. It is pointed out that the design of the search favors detection of companions with a relatively large separation from the primary star; hence the result indicates that there are few or no black-dwarf companions beyond about 10 arcsec from nearby stars.