A pseudoclassical theory of a Weyl particle in a spacetime of dimensio
n D = 2n is constructed. The canonical quantization of this pseudoclas
sical theory is carried out; it results in the theory of a D = 2n dime
nsional Weyl particle in the Foldy-Wouthuysen representation. The quan
tum mechanics of the neutral Weyl particle in an even-dimensional spac
etime is constructed, and connections of this theory with the quantum
field theory of a Majorana-Weyl particle are discussed for D = 10.