  For the two-parameter $p,q$-deformed Heisenberg algebra introduced recently
and in which, instead of usual commutator of $X$ and $P$ in the l.h.s. of basic
relation $[X,P] = {\rm i}\hbar$, one uses the $p,q$-commutator, we established
interesting properties. Most important is the realizability of the
$p,q$-deformed Heisenberg algebra by means of the appropriate deformed
oscillator algebra. Another uncovered property is special extension of the
usual mutual Hermitian conjugation of the creation and annihilation operators,
namely the so-called $\eta(N)$-pseudo-Hermitian conjugation rule, along with
the related $\eta(N)$-pseudo-Hermiticity property of the position or momentum
operators. In this work, we present some new solutions of the realization
problem yielding new (nonstandard) deformed oscillators, and show their
inequivalence to the earlier known solution and the respective deformed
oscillator algebra, in particular what concerns ground state energy.
