[en] The problems of the classical dynamics of a relativistic string are related to the theory of two-dimensional extremal surfaces in n-dimensional pseudo-Euclidean space Esub(n)sup(1). In the three-dimensional space-time E₃¹ one can use the Gaussian theory of two-dimensional surfaces when a surface is defined by the first and second quadratic form. By integrating the derivational formulae for the basic vectors one can obtain the representations for these vectors in a certain basis, which satisfy the orthonormal gauge and d'Alembert equation in the dynamics of string. These representations allow the generalizations to the pseudo-Euclidean space Esub(n)sup(') of any dimensionality n. A representation containing n-2 arbitrary functions and satisfying the gauge conditions, equations of motion and boundary conditions for the free string is obtained for the relativistic string in the space