  The subject of this paper is degenerate integrability in Hamiltonian
mechanics. It starts with a short survey of degenerate integrability. The first
section contains basic notions. It is followed by a number of examples which
include the Kepler system, Casimir models, spin Calogero models, spin
Ruijsenaars models, and integrable models on symplectic leaves of Poisson Lie
groups. The new results are degenerate integrability of relativistic spin
Ruijsenaars and Calogero-Moser systems and the duality between them.
