Teleological variations of non-deterministic processes are defined. The immediate past of a system defines the state from which the ordinary (non-teleological) dynamical law governing the system derives different possible present states. For every possible present state, again a number of possible states for the next time step can be defined, and so on. After k time steps, a selection criterion is applied. The present state leading to the selected state after k time steps is taken to be the effective present (...) state. Hence, the present state of a system is defined by its past in the sense that the past determines the possible states that are to be considered, and by its future in the sense that the selection of a possible future state determines the effective present state. A system that obeys this type of teleological dynamics may have significantly better performance than its non-teleological counterpart. The basic reason is that evolutions that are less optimal for the present time step, but which lead to a higher optimality after k time steps, may be preferred. This abstract concept of teleology is implemented for two concrete systems. First, it is applied to a general method for function approximation and classification problems. The method at issue treats all problems handled by conventional connectionism, and is suited for information with inner structure also. Second, it is applied to a dynamics in which forms of maximal homogeneity have to be produced. The relevance of the latter dynamics for generative art is illustrated. The teleology is `deep' in the sense that it is situated at the cellular level, in contradistinction with the teleology that is usually met in cognitive contexts, and which refers to macroscopic processes such as making plans. It is conjectured that deep level teleology is useful for machines, even though the issue if natural systems use this teleology is left open. (shrink)