We prove existence of quasiperiodic breathers in Hamiltonian lattices
of weakly coupled oscillators having some integrals of motion independent
of the Hamiltonian. The proof is obtained by constructing quasiperiodic
breathers in the anticontinuoum limit and using a recent theorem by N.N.
Nekhoroshev  as extended in  to continue them to the coupled case. Applications
to several models are given.