  Interrelation between the two-particle and mean-field problems is used to
describe the strong pseudogap and superconducting states in cuprates. We
present strong pseudogap state as off-diagonal short-range order (ODSRO)
originating from quasi-stationary states of the pair of repulsing particles
with large total momentum (K - pair). Phase transition from the ODSRO state
into the off-diagonal long-range ordered (ODLRO) superconducting state is
associated with Bose-Einstein condensation of the K - pairs. A checkerboard
spatial order observable in the superconducting state in the cuprates is
explained by a rise of the K - pair density wave. A competition between the
ODSRO and ODLRO states leads to the phase diagram typical of the cuprates.
Biordered superconducting state of coexisting condensates of Cooper pairs with
zero momentum and K - pairs explains some properties of the cuprates observed
below Tc: Drude optical conductivity, unconventional isotope effect and two-gap
quasiparticle spectrum with essentially different energy scales.
