  A pseudoclassical theories of Majorana, Weyl and Majorana--Weyl particles in
the space--time dimensions $D=2n$ are constructed. The canonical quantization
of these theories is carried out and as a result we obtain the quantum
mechanical description of neutral particle in $D=2n$ , Weyl particle in $D=2n$
and neutral Weyl particle in $D=4n+2$. In $D=2,4({\rm mod}8)$ dimensional
space--time the description of the neutral particle coincides with the field
theoretical description of the Majorana particle in the Foldy--Wouthuysen
representation. In $D=8k+2$ dimensions the neutral Weyl particle coincides with
the Majorana--Weyl particle in the Foldy--Wouthuysen representation.
