We consider models, in which stability of Dark Matter particles D is ensured by the conservation of the new quantum number, called D-parity here. Our models contain also charged D-odd particle D±. We propose method for precision measuring masses and spin of D-particles via the study of energy distribution of single lepton (e or μ) in the process e+e– → D+D– → DDW+W– with the observable state dijet + μ (or e) + nothing. It is shown that this distribution has kinematically determined singular points (upper edge and kinks or peak). Measuring of their positions allow to determine precisely masses of D and D±. After this, even a rough measuring of corresponding cross section allows to determine the spin of D particles.