Continuous, dynamic and short-term learning is an effective learning strategy when operating in very fast and dynamic environments, where concept drift constantly occurs. In an on-line, stream learning model, data arrives as a stream of sequentially ordered samples, and older data is no longer available to revise earlier suboptimal modeling decisions as the fresh data arrives. Learning takes place by processing a sample at a time, inspecting it only once, and as such, using a limited amount of memory; stream approaches work in a limited amount of time, and have the advantage of performing a prediction at any point in time during the stream. We focus on a particularly challenging problem, that of continually learning detection models capable to recognize cyber-attacks and system intrusions in a highly dynamic environment such as the Internet. We consider adaptive learning algorithms for the analysis of continuously evolving network data streams, using a dynamic, variable length system memory which automatically adapts to concept drifts in the underlying data. By continuously learning and detecting concept drifts to adapt memory length, we show that adaptive learning algorithms can continuously realize high detection accuracy over dynamic network data streams.