SU(N) confining strings

String representations of the SU(N)-version of compact QED in three and four dimensions are constructed. Using for concreteness the three-dimensional case, it is demonstrated how the resulting SU(N)-generalization of the so-called theory of confining strings can be obtained in various ways. Such an SU(N)-theory of confining strings is then compared with the approach to the derivation of the string tension of the Wilson loop defined at the flat contour. This approach is based on the evaluation of the mean magnetic field inside the contour. In the SU(N)-version of the four-dimensional compact QED with the θ-term, the critical values of the θ-parameter, at which the problem of crumpling of large world sheets might be solved, are found. These values are only accessible provided the electric coupling constant is larger than a certain N -dependent quantity. This parallels the fact that confinement in the four-dimensional compact QED holds in the strong-coupling regime.