Quantum string theory in indefinite space of states

The quantum string theory in indefinite (pseudo-Hilbert) Fock representation is considered. It is shown that all anomalies in 4-dimensional theory of open bosonic string are cancelled at particular choice of vacuum state. In this the algebra of reparametrizations (in covariant approach) and the algebra of rotations (in light cone gauge) become closed. The indefiniteness of the state space introduces some non-physical features into the theory. Modifications of the given method are discussed, which are necessary to construct more realistic theory.