The Liouville equation is considered for the statistical system consisting of identical constructureless free particles and grains initially. It relaxes then due to a collection of the particles by the grains. Dusty plasmas are particular cases of this system. The free and collected particles are considered as a common sub-system which is described by the common whole distribution function. It is shown that this sub-system is described by the complex integral-differential equation which can be expected to lead to Non-Markovian kinetics. Computer modeling shows that background electrons and ions can be non-ideal components of relaxing dusty plasmas in plasma crystals due to the intensive charge exchange of electrons and ions with dust particles even in the cases where their numbers in the Debye cube are large. The selective collection of electrons and ions by dust particles causes their deviation from the initial equilibrium as well as the non-equilibrium evolution of the self-consistent electric potential and electric charge of dust particles.