Summary: The authors study the correspondence between the ‘relativistic spin-foam’ model introduced by J. W. Barrett and L. Crane [J. Math. Phys. 39, 3296-3302 (1998)], J. Baez [Classical Quantum Gravitity 15, 1827-1858 (1998; Zbl 0932.83014)] and the \(so(4)\) Plebański action [J. F. Plebański, J. Math. Phys. 18, 2511-2520 (1977; Zbl 0368.53032)]. They argue that the \(so(4)\) Plebański model is the continuum analogue of the relativistic spin-foam model. They prove that the \(so(4)\) Plebański action possesses four phases, one of which is related to gravity and discuss the relation between this model and the model of Euclidean tetrad gravity. They also show that the \(so(4)\) Plebański model possesses another natural discretization that can be associated with another, new, spin-foam model which appear to be the \(so(4)\) counterpart of the spin-foam model describing the self-dual formulation of gravity.