  The most common nonlinear deformations of the su(2) Lie algebra, introduced
by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and
include the quantum algebra su_q(2) as a special case. In the present
contribution, less common nonlinear deformations of su(2), introduced by
Delbecq and Quesne and involving two deforming functions of J_0, are reviewed.
Such algebras include Witten's quadratic deformation of su(2) as a special
case. Contrary to the former deformations, for which the spectrum of J_0 is
linear as for su(2), the latter give rise to exponential spectra, a property
that has aroused much interest in connection with some physical problems.
Another interesting algebra of this type, denoted by ${\cal A}^+_q(1)$, has two
series of (N+1)-dimensional unitary irreducible representations, where N=0, 1,
2, .... To allow the coupling of any two such representations, a generalization
of the standard Hopf axioms is proposed. The resulting algebraic structure,
referred to as a two-colour quasitriangular Hopf algebra, is described.
