  We present an extension of the theory known as Lin's method to heteroclinic
chains that connect hyperbolic equilibria and hyperbolic periodic orbits. Based
on the construction of a so-called Lin orbit, that is, a sequence of continuous
partial orbits that only have jumps in a certain prescribed linear subspace,
estimates for these jumps are derived. We use the jump estimates to discuss
bifurcation equations for homoclinic orbits near heteroclinic cycles between an
equilibrium and a periodic orbit (EtoP cycles).
