SU(N) confining strings

String representation of the SU(N)-version of compact QED in three dimensions is constructed. It is demonstrated how the resulting SU(N)-generalization of the so-called theory of confining strings can be obtained in various ways. In its weak-field limit (corresponding to the limit of low monopole densities), this theory enables one to fix the value of the string tension, which cannot be fixed when being deduced from the mean magnetic field inside a flat contour. Moreover, the obtained theory enables one to find also the coupling constants of the terms in the expansion of the nonlocal string effective action which are higher in the derivatives than the Nambu-Goto term (some of which vanish at the flat surface). (author)