First integrals generated by pseudosymmetries in Nambu-Poisson mechanics

Some types of first integrals for Hamiltonian Nambu-Poisson vector fields are obtained by using the notions of pseudosymmetries. In this theory, the homogeneous Hamiltonian vector fields play a special role and we point out this fact. The differential system which describe the $SU(2)$-monopoles is given as example. The paper ends with two appendices.