  We investigate string solutions to the classical equations of motion
("classical QCD strings") for a dual Ginzburg-Landau model corresponding to
SU(3) gluodynamics in an abelian projection. For a certain relation between
couplings of the model the string solutions are defined by first order
differential equations. These solutions are related to vortex configurations of
the Abelian Higgs model in the Bogomol'ny limit. An analytic expression for the
string tension is derived and the string-string interactions are discussed. Our
results imply that the vacuum of SU(3) gluodynamics is near a border between
type-I and type-II dual superconductivity.
