Nonlinear delay-diffusion equations of the form
are studied and stability and bifurcation results are obtained by studying the perturbation of the spectrum of the linearization
caused by . It is shown that a centre manifold of any dimension exists for some , , and . Moreover, it is shown that if are the pure imaginary eigenvalues of the linearized equation, then the numbers are rationally independent and as increases through the critical value, the nonlinear equation undergoes a bifurcation from eigenvalues, where is the sum of the multiplicities of the eigenvalues.