  We present three groups of noncanonical quantum oscillators. The position and
the momentum operators of each of the groups 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 statistictics. The internal angular momentum $s$ of
the $osp(3/2)$-oscillators takes no more than three (half)integer values. In a
particular representation $s=1/2$.
