A cohesive zone model is developed to describe the adhesion between long cylinders in contact, thus extending the work of Maugis, who considered the adhesion of spheres. A parameter lambda is shown to govern the range of applicability of the different contact theories, and an explicit condition is given for the use of the Johnson-Kendall-Roberts (JKR) approach. An interesting result is that unlike the situation in the three-dimensional problem, the Derjaguin-Muller-Toporov (DMT) solution is not approached as lambda --> 0. Instead, it is when lambda is of order 1 that an approximation similar to the DMT theory can be used.