In this paper, we introduce a novel form of association rules (ARs) that do not require discretization of continuous variables or the use of intervals in either sides of the rule. This rule form captures nonlinear relationships among variables, and provides an alternative pattern representation for mining essential relations hidden in a given data set. We refer to the new rule form as a functional AR (FAR). A new neural network-based, co-operative, coevolutionary algorithm is presented for FAR mining. The algorithm is applied to both synthetic and real-world data sets, and its performance is analyzed. The experimental results show that the proposed mining algorithm is able to discover valid and essential underlying relations in the data. Comparison experiments are also carried out with the two state-of-the-art AR mining algorithms that can handle continuous variables to demonstrate the competitive performance of the proposed method.