  We develop a time-non-local (TNL) formalism based on variational calculus,
which allows for the analysis of TNL Lagrangians. We derive the generalized
Euler-Lagrange equations starting from the Hamilton's principle and, by
defining a generalized momentum, we introduce the corresponding Hamiltonian
formalism. We apply the formalism to second order TNL Lagrangians and we show
that it reproduces standard results in the time-local limit. An example will
show how the formalism works, and will provide an interesting insight on the
non-standard features of TNL equations.
