In a multi-feed small-diameter circular knitting machine provided with needles (4), jacks (5) and selectors (6), the selector raising cams (14) have a smaller height than the jack raising cams, so that the selectors (6) return to their selection position while the jacks (5) are still descending. The selectors (6) and jacks (5) therefore move independently after an initial raising by the selectors (6) acting on the jacks (5). The selectors (6) move within a cylinder trick portion (3a) which lies at a greater distance from the cylinder axis than the trick portion (3b) within which the needles (4) and jacks (5) move, and comprise an appendix (21) extending towards the needle cylinder (2) for engaging the jacks (5). The machine can have a larger number of selection positions than know machines for the same needle circle diameter and fineness.