Coexistence of Non-Conventional Condensates in Two-Level Bose Atom System

In the framework of the Bogolyubov approximation and using the Bogolyubov inequalities we give a simple proof of the coexistence of two non-conventional Bose-Einstein condensates in the case of some superstable Bose system whose atoms have an internal two-level structure and their energy operators in the second quantized form depend on the number operators only.