ANN design is usually thought as a training problem to be solved for some predefined ANN structure and connectivity. Training methods are very problem and ANN dependent. They are sometimes very accurate procedures but they work in narrow and restrictive domains. Thus the designer is faced to a wide diversity of multimodal and different training mechanisms. We have selected Genetic Algorithms as training procedures because of their robutness and their potential application to any ANN type training. Furthermore we have addressed the connectivity and structure definition problems in order to accomplish a full genetic ANN design. These three levels of design can work in parallel, thus achieving multilevel relationships to yield better ANNs. GRIAL is the tool used to test several new and known genetic techniques and operators. PARLOG is the Concurrent Logic Language used for the implementation in order to introduce new models for the genetic work and attain an intralevel distributed search as well as to parallelize any ANN evaluation.