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The aim of this work is to achieve a formulation of the bosonic string theoryin which T-duality appears as a manifest symmetry. Two models exhibiting thisproperty are discussed. The first is based on the stringy extension of theFloreanini-Jackiw Lagrangians for chiral fields and is characterized by theloss of manifest covariance on the world-sheet, recovered on mass-shell. Thesecond model exhibits two-dimensional covariance while doubling a priori thestring coordinates in the target space. They are shown to be equivalent.

Two Double String Theory Actions: Non-Covariance vs. Covariance