a.k.a. Rubik's Rings
Designed by E. Pap, made by Politoys in Hungary, 1982.
(left, plastic, 3.1 by 4.9 by 1/2 inches,
right is identical to left but with different colored balls,
bottom version circa 2000 is 3-dimensional but works the same way)

An old puzzle similar to this (the Race War Puzzle), with 22 balls in a ring and each ring one color, is shown on Page 131 of the Slocum and Sonneveld Fifteen book, and the mechanism is presented in the 1892 patent of W. Churchill.

Further Reading
Jaap's Page, from: www.geocities.com/jaapsch/puzzles/rings.htm
Churchill Patent, from: www.uspto.gov - patent no. 507,215