  We establish explicitely the relation between the algebraic and Nambu-Goto
strings when the target space is a four dimensional flat space. We find that
the two theories are exactly equivalent only when the algebraic string is
restricted to the self-dual or anti self-dual sectors. In its Hamiltonian
formulation, the algebraic string defines a constrained system with first and
second class constraints. In the self-dual case, we exhibit the appropriate set
of second class constraints such that the resulting physical phase space is
formulated in the same way as it is in the standard Nambu-Goto string. We
conclude with a discussion on alternative quantisation schemes.
