An n-affine manifold is a differentiable manifold endowed with an atlas whose transition functions are locally affine transformations of ℝn . The paper studies affine dynamic, that is, affine endomorphisms of affine manifolds. The main goal is to relate the dynamical viewpoint to the completeness problem. In particular, it is shown that the Markus conjecture is true when dim Aff(M, [dtri ]) > dim M − 2.