  We investigate the canonical aspects of the algebraic first order formulation
of strings introduced two decades ago by Balachandran and collaborators. We
slightly enlarge the Lagrangian framework and show the existence of a self-dual
formulation and of an Immirzi-type parameter reminiscent of four-dimensional
first order gravity. We perform a full Hamiltonian analysis of the self-dual
case: we extract the first class constraints and construct the Dirac bracket
associated to the second class constraints. The first class constraints contain
the diffeomorphisms algebra on the world-sheet, and the coordinates are shown
to be non-commutative with respect to the Dirac bracket. The Hamilton equations
in a particular gauge are shown to reproduce the wave equation for the string
coordinates. In the general, non-self-dual case, we also explicit the first
class constraints of the system and show that, unlike the self-dual
formulation, the theory admits an extra propagating degree of freedom than the
two degrees of freedom of conventional string theory. This prevents the general
algebraic string from being strictly equivalent to the Nambu-Goto string.
