  The problem of generating discrete superpositions of coherent states in the
process of light propagation through a nonlinear Kerr medium, which is modelled
by the anharmonic oscillator, is discussed. It is shown that under an
appropriate choice of the length (time) of the medium the superpositions with
both even and odd numbers of coherent states can appear. Analytical formulae
for such superpositions with a few components are given explicitly. General
rules governing the process of generating discrete superpositions of coherent
states are also given. The maximum number of well distinguished states that can
be obtained for a given number of initial photons is estimated. The
quasiprobability distribution $Q(\alpha,\alpha^*,t)$ representing the
superposition states is illustrated graphically, showing regular structures
when the component states are well separated.
