  In this paper, we establish some Harnack type inequalities satisfied by
positive solutions of nonlocal inhomogeneous equations arising in the
description of various phenomena ranging from population dynamics to
micro-magnetism. For regular domains, we also derive an inequality up to the
boundary. The main difficulty in such context lies in a precise control of the
solutions outside a compact set and the existence of local uniform estimates.
We overcome this problem by proving a contraction result which makes the $L^1$
norms of the solutions on two compact sets $\o_1\subset\subset\o_2$ equivalent.
We also construct the principal positive eigenfunctions associated to
particular nonlocal operators by using the corresponding Harnack type
inequalities.
