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In many models stability of Dark Matter particles $D$ is ensured byconservation of a new quantum number referred to as $D$-parity. Our models alsocontain charged $D$-odd particles $D^\pm$ with the same spin as $D$. Here wepropose a method to precisely measure the masses and spins of $D$-particles inthe process $\epe\to D^+D^-\to DDW^+W^-\to DD (q\bar{q})(\ell\nu)$ with asignature {\it dijet + $\mu$ (or $e$) + nothing}. It is shown that the energydistribution of the lepton has singular points (upper edge and kinks or a peak)whose positions are kinematically determined. For precise determination of $D$and $D^\pm$ masses, it is sufficient to measure these singular points and upperedge of dijet energy spectrum. After this procedure, even an approximatemeasurement of the corresponding cross section allows a determination of thespin of $D$ particles to be performed.  New points of this work are: 1) We propose to use only the well measurableenergy spectra of {\bf individual leptons} and the upper edge of the dijetenergy spectrum. 2) We propose to identify the spin of $D$-particles via valueof the cross section for the discussed process.

Measuring mass and spin of Dark Matter particles with the aid energy spectra of single lepton and dijet at the $e^+e^-$ Linear Collider