  A scheme is proposed which allows to obtain special $q$-oscillator models
whose characteristic feature consists in possessing two differing pairs of
degenerate energy levels. The method uses the model of two-parameter deformed
$q,p$-oscillators and proceeds via appropriately chosen particular relation
between $p$ and $q$. Different versions of quadratic relations $p=f(q)$ are
utilized for the case which implies two degenerate pairs $E_1=E_2$ and
$E_3=E_4$. On the other hand, using one fixed quadratic relation, we obtain
$p$-oscillators with other cases of two pairs of (pairwise) degenerate energy
levels.
