A novel hyperellipsoidal clustering technique is presented for an intrusion-detection system in network security. Hyperellipsoidal clusters toward maximum intracluster similarity and minimum intercluster similarity are generated from training data sets. The novelty of the technique lies in the fact that the parameters needed to construct higher order data models in general multivariate Gaussian functions are incrementally derived from the data sets using accretive processes. The technique is implemented in a feedforward neural network that uses a Gaussian radial basis function as the model generator. An evaluation based on the inclusiveness and exclusiveness of samples with respect to specific criteria is applied to accretively learn the output clusters of the neural network. One significant advantage of this is its ability to detect individual anomaly types that are hard to detect with other anomaly-detection schemes. Applying this technique, several feature subsets of the tcptrace network-connection records that give above 95% detection at false-positive rates below 5% were identified.