  It is shown that Nambu-Poisson and Nambu-Jacobi brackets can be defined
inductively: a n-bracket, n>2, is Nambu-Poisson (resp. Nambu-Jacobi) if and
only if fixing an argument we get a (n-1)-Nambu-Poisson (resp. Nambu-Jacobi)
bracket. As a by-product we get relatively simple proofs of Darboux-type
theorems for these structures.
