  Expressions for variables of the center of mass and relative motions for
two-body system with different and equal masses in three-dimensional spaces of
constant curvature are introduced in the terms of biquaternions. The problem of
the separation of center mass and relative motion variables for action of two
particles into biquaternionic form is formulated. We showed that the algebraic
nature of these nonseparable variables follows from the fact that algebra of
biquaternions is noncommutative. Some special cases of separation of center
mass and relative motion variables are considered.
