This paper addresses the task of detecting intrusions in the form of malicious programs on a host computer system by inspecting the trace of system calls made by these programs. We use "attack-tree" type generative models for such intrusions to select features that are used by a Support Vector Machine Classifier. Our approach combines the ability of an HMM generative model to handle variable-length strings, i.e. the traces, and the non-asymptotic nature of Support Vector Machines that permits them to work well with small training sets.