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For string theory on AdS3 with pure NS-NS flux a complete set of DDF operators is constructed, from which one can read off the symmetry algebra of the spacetime CFT. Together with an analysis of the spacetime spectrum, this allows us to show that the long string sector of superstring theory on AdS3×S3×T4 for generic NS-NS flux is described by the symmetric orbifold of (N=4Liouville theory)×T4. For the case of minimal flux (k=1), the Liouville factor disappears, and we just obtain the symmetric orbifold of T4, thereby giving further support to a previous claim. We also show that a similar analysis can be done for bosonic string theory on AdS×3X.