  In a series of recent papers one of us has analyzed in some details a class
of elementary excitations called {\em pseudo-bosons}. They arise from a special
deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is
replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here,
after a two-dimensional extension of the general framework, we apply the theory
to a generalized version of the two-dimensional Hamiltonian describing Landau
levels. Moreover, for this system, we discuss coherent states and we deduce a
resolution of the identity. We also consider a different class of examples
arising from a classical system, i.e. a damped harmonic oscillator.
