  The light-cone Hamiltonian is derived from the general gauge -- and Lorentz
-- invariant expression for the $q\bar{q}$ Green's function, containing
confinement via the area law for the Wilson loop.The resulting Hamiltonian
contains in a nonadditive way contributions from quark and string degrees of
freedom. Different limiting dynamical regimes of the system of quarks connected
by the string are found. In the limit of no transverse motion one recovers the
t'Hooft's 1+1 QCD Hamiltonian. The correspondence with the rest frame
Hamiltonian spectrum is established. The important notion of the light-cone
string, contributing significantly to the energy--momentum is discussed.
