We investigate a dual Higgs model with dual Dirac strings invariant un
der U(1) gauge transformations, where U(1) is the Abelian gauge group
of dual-vector potential transformations spontaneously broken by the H
iggs mechanism. The action of a dual Dirac string calculated in leadin
g order in the large Higgs field mass expansion coincides with a dual
version of that obtained by Nambu. For the example of the string tensi
on at the classical tree-level approach we develop a procedure for the
computation of contributions of string-string interactions. Non-pertu
rbative phenomena of compact QED are discussed.