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We present the string Lagrangian with manifest T-duality. Not only zero-modesbut also all string modes are doubled. The gravitational field is an O(D,D)gauge field. We give a Lagrangian version of the section condition for thegauge invariance which compensates the O(D,D) transformation from thegravitational field and the GL(2D) coordinate transformation. We also show thegauge invariance of the line element of the manifest T-duality space and theO(D,D) condition on the background. Different sections describe dual spaces.

O(D,D) gauge fields in the T-dual string Lagrangian