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We present a phase diagram for a dilute two-dimensional Bose-gas on alattice. For one sort of boson we consider a realistic case of the van derWaals interaction between particles with a strong hard-core repulsion $U$ and avan der Waals attractive tail $V$. For $V< 2 t $, $t$ being a hoppingamplitude, the phase diagram of the system contains regions of the usualone-particle Bose-Einstein condensation (BEC). However for $V>2t$ we have totalphase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For twosorts of structureless bosons described by the two band Hubbard model an s-wavepairing of the two bosons of different sort $<b_1 b_2 > \neq 0$ is possible.The results we obtained should be important for different Bose systems,including submonolayers of $^4$He, excitons in semiconductors, Schwinger bosonsin magnetic systems and holons in HTSC. In the HTSC case a possibility oftwo-holon pairing in the slave-bosons theories of superconductivity can restorea required charge $2e$ of a Cooper pair.Comment: 10 pages, 2 figure

Two-particle pairing and phase separation in a two-dimensional Bose gas with one or two sorts of bosons