  The paper presents a review of results concerning the non-conventional
dynamical condensation versus conventional Bose-Einstein condensation,
including the case of generalised van den Berg-Lewis-Pul\'e condensate. The
review is based on detailed discussion of two models: a simple toy model and
the Bogoliubov Weakly Imperfect Bose-Gas model, which was invented for
explanation of superflfluidity of liquid 4He, but which is also instructive for
analysis of non-conventional condensation regarding some recent interpretations
of experimental data.
