X-ray scattering studies were performed to elucidate the structure and the character of the correlations in a mesophase with two-dimensional positional order formed in a side group polymer. X-ray diffraction patterns of oriented fibres display weak diffuse lines in the direction parallel to the orientation of the side groups and a regular pattern of strong diffuse spots in the perpendicular direction, indicating positional order on the local scale. The side groups are close packed within a two-dimensional (2D) centred orthorhombic lattice and are tilted with respect to their nearest neighbours. The positional order is anisotropic and is limited by a correlation length of about 30-40A, that is approximately six involved in the short range order. In the direction along the normal to the 2D system shows no translational order. This phase displays the same unit cell symmetry and direction of tilt as the layers of the K phase and is designated as TDK, where the first two letters stand for 'two-dimensional'. Unexpectedly, we found a regular pattern of weak diffuse spots in the small angle scattering region. These indicate a short range modulated structure with the vector of modulation lying in the plane of the 2D packing of the side chains is proposed to explain the formation of modulated structure and the anisotropic character of the positional correlations. to eight side groups are plane, the order. A simple model of the