  Coherent states are usually defined as eigenstates of an unbounded operator,
the so-called annihilation operator. We propose here possible constructions of
{\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a
\underline{bounded} operator related to an annihilation-like operator. We use
this bounded operator to construct a sort of modified harmonic oscillator and
we analyze the dynamics of this oscillator from an algebraic point of view.
