  In a recent paper a pair of operators $a$ and $b$ satisfying the equations
$a^\dagger a=bb^\dagger+\gamma\1$ and $aa^\dagger=b^\dagger b+\delta\1$, has
been considered, and their nature of ladder operators has been deduced and
analysed. Here, motivated by the spreading interest in non self-adjoint
operators in Quantum Mechanics, we extend this situation to a set of four
operators, $c$, $d$, $r$ and $s$, satisfying $ dc=rs+\gamma\1$ and
$cd=sr+\delta\1$, and we show that they are also ladder operators. We show
their connection with biorthogonal families of vectors and with the so-called
$\D$-pseudo bosons. Some examples are discussed.
