I report on suspected nearby stars with proper motions 1.0 arcsec > μ ≥ 0.5 arcsec/yr in the southern sky (DEC = −90° to 00°). This sample of slow-motion (SLOWMO) stars complements the work of Jao (2004), who reported on faster moving stars with μ ≥ 1.0 arcsec/yr in the entire sky for his doctoral dissertation, and the work of Finch (2007), who uncovered stars moving slower than 0.5 arcsec/yr between declinations −90° and −47°. Characterizations of SLOWMO systems include trigonometric parallaxes, optical and infrared photometry. For stars without trigonometric parallaxes, colors and apparent magnitudes are used to calculate photometric distance estimates and the statistics of this population of stars are analyzed. The SLOWMO sample is comprised of 1906 total stars − 560 estimated to be less than 25 parsecs away, and 245 stars without parallaxes estimated to be within 25 parsecs.