  We study Lagrangian systems with a finite number of degrees of freedom that
are non-local in time. We obtain an extension of Noether theorem and Noether
identities to this kind of Lagrangians. A Hamiltonian formalism is then set up
for this systems. $n$-order local Lagrangians can be treated as a particular
case and the standard results for them are recovered. The method is then
applied to several other cases, namely two examples of non-local oscillators
and the p-adic particle.
