This thesis concerns anomaly detection as a mechanism for intrusion detection in a machine learning framework, using two kinds of audit data : system call traces and Unix shell command traces. Anomaly detection systems model the problem of intrusion detection as a problem of self-nonself discrimination problem. To be able to use machine learning algorithms for anomaly detection, precise definitions of two aspects namely, the learning model and the dissimilarity measure are required. The audit data considered in this thesis is intrinsically sequential. Thus the dissimilarity measure must be able to extract the temporal information in the data which in turn will be used for classification purposes. In this thesis, we study the application of a set of dissimilarity measures broadly termed as sequence kernels that are exclusively suited for such applications. This is done in conjunction with Instance Based learning algorithms (IBL) for anomaly detection. We demonstrate the performance of the system under a wide range of parameter settings and show conditions under which best performance is obtained. Finally, some possible future extensions to the work reported in this report are considered and discussed.