It is possible to predict future life forms? In this paper it is argued that the answer to this question may well be positive. As a basis for predictions a rationale is used that is derived from historical data, e.g. from a hierarchical classification that ranks all building block systems, that have evolved so far. This classification is based on specific emergent properties that allow stepwise transitions, from low level building blocks to higher level ones. This paper shows how this (...) hierarchy can be used for predicting future life forms.The extrapolations suggest several future neural network organisms. Major aspects of the structures of these organisms are predicted. The results can be considered of fundamental importance for several reasons. Firstly, assuming that the operator hierarchy is a proper basis for predictions, the result yields insight into the structure of future organisms. Secondly, the predictions are not extrapolations of presently observed trends, but are fully integrated with all historical system transitions in evolution. Thirdly, the extrapolations suggest the structures of intelligences that, one day, will possess more powerful brains than human beings.This study ends with a discussion of possibilities for falsification of the present theory, the implications of the present predictions in relation to recent developments in artificial intelligence and the philosophical implications of the role of humanity in evolution with regard to the creation of future neural network organisms. (shrink)