  We discuss BEC in (quasi)2D trapped gases and find that well below the
transition temperature $T_c$ the equilibrium state is a true condensate,
whereas at intermediate temperatures $T<T_c$ one has a quasicondensate
(condensate with fluctuating phase). The mean-field interaction in a quasi2D
gas is sensitive to the frequency $\omega_0$ of the (tight) confinement in the
"frozen" direction, and one can switch the sign of the interaction by changing
$\omega_0$. Variation of $\omega_0$ can also reduce the rates of inelastic
processes, which opens prospects for tunable BEC in trapped quasi2D gases.
