Abstract
We present three groups of non-canonical quantum oscillators. The position and momentum operators of each group generate basic Lie superalgebras, namely sl(1/3), osp(1/6) and osp(3/2). The sl(1/3) oscillators have finite energy spectrum and finite dimensions. The osp(1/6) oscillators are related to the para-Bose statistics. The internal angular momentum s of the osp(3/2) oscillators takes no more than three (half)integer values. In a particular representation s=1/2.