We show that the quasi-exponential solution exp (Bt - At2) of R + alph
aR2 gravity is an attractor for all homogeneous and isotropic solution
s of higher order gravity theories derived from a lagrangian that is a
n arbitrary analytic function of the scalar curvature R. This indicate
s that a generalized form of the cosmic no-hair conjecture is valid in
the framework of higher order gravity theories.