  The general analysis of the relations between masses and angular momenta in
the configurations composed of two balancing extremal Kerr particles is made on
the basis of two exact solutions arising as extreme limits of the well-known
double-Kerr spacetime. We show that the inequality M^2 >= |J| characteristic of
an isolated Kerr black hole is verified by all the extremal components of the
Tomimatsu and Dietz-Hoenselaers solutions. At the same time, the inequality can
be violated by the total masses and total angular momenta of these binary
systems, and we identify all the cases when such violation occurs.
