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We consider models in which stability of Dark Matter particles $D$ is ensuredby the conservation of the new quantum number, called D-parity here. Our modelscontain also charged $D$-odd particle $D^\pm$.  Here I propose the method for precision measuring masses and spin of$D$-particles via the study of energy distribution of single lepton ($e$ or$\mu$) in the process $\epe\to D^+D^-\to DDW^+W^-$ with the observable states{\it dijet + lepton} ($\mu$ or $e$) + {\it nothing}. To determine preciselymasses of $D$ and $D^\pm$, it is sufficient to measure the singular points inthe lepton energy distributions (upper edge and kinks or peak). After this,even a rough measuring of corresponding cross section allows to determine thespin of $D$ particles.  This approach is free from the difficulties of a well-known methods ofmeasuring the masses via the edges of the energy distribution of dijets,representing $W$, which obliged by inaccuracies in measuring the energies ofindividual jets.

Singularities in the single lepton energy spectrum for precise measuring mass and spin of Dark Matter particles at the e^+e^- Linear Collider