  This work describes the formulation of the manifestly ghost-free (spacetime)
light-cone gauge for bosonic string theory with non-trivial spacetime metric,
antisymmetric tensor, dilaton and tachyon fields. The action is a general
two-dimensional sigma model, corresponding to a closed string theory with a
second order action in the Polyakov picture. The spacetime fields must have a
symmetry generated by a null, covariantly constant spacetime vector in order
for the light-cone gauge to be accessible. Also, the theory must be Weyl
invariant. The conditions for Weyl invariance are computed within the
light-cone gauge, reproducing the usual beta functions. The calculation of the
dilaton beta function and the critical dimension is somewhat novel in this
ghost-free theory. Some exactly solvable light-cone theories are discussed.
