Lin's method and homoclinic bifurcations for functional differential equations of mixed type H. J. HupkesS. Verduyn Lunel 34K1834K1734K1937G15mixed type functional differential equationhomoclinic bifurcationLin's methodorbit-flip bifurcationfinite dimensional reductionexponential dichotomiesadvanced and retarded arguments We extend Lin's method for use in the setting of parameter-dependent nonlinear functional differential equations of mixed type (MFDEs). We show that the presence of $M$-homoclinic and $M$-periodic solutions that bifurcate from a prescribed homoclinic connection can be detected by studying a finite dimensional bifurcation equation. As an application, we describe the codimension two orbit-flip bifurcation in the setting of MFDEs. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3661 10.1512/iumj.2009.58.3661 en Indiana Univ. Math. J. 58 (2009) 2433 - 2488 state-of-the-art mathematics http://iumj.org/access/