We consider homeomorphism f of a torus which is isotopic to a Dehn twist. Certain periodic orbits for f, with a particularly simple behaviour of f in the complement of the orbit, are called simple. Certain pairs of such orbits are called simple pairs. Their rotation numbers (rational numbers a/b and c/d) are Farey neighbors which means |ad-bc|=1. We prove that if there exists such simple pair of periodic orbits for f then f is pseudo-Anosov in the complement of the orbits and for every rational number q between a/b and c/d there exists a simple periodic orbit for f with rotation number q and for every pair of rational numbers q,p which are Farey neighbors and lie between a/b and c/d there exists a simple pair of periodic orbits for f with rotation numbers q and p respectively.