Affective Computing is a newly emerging field which has been defined as ``computing that relates to, arises from, or deliberately influences emotions.'' Many applications in affective computing research rely on, or can greatly benefit from, information regarding affective states of computer users. The sensing and recognition of human affect, therefore, is one of the most important research areas to receive much attention in the area of affective computing. In this work, inspired by the particular application of human-machine interaction and the potential use that human-computer interfaces can make of knowledge regarding the affective state of a user, we investigate the problem of sensing and recognizing typical affective experiences that arise in this setting. In particular, through the design of experimental conditions for data gathering, we approach the problem of detecting ``frustration'' in human computer interfaces. By first sensing human biophysiological correlates of internal affective states, we proceed to stochastically model the biological time series with Hidden Markov Models to obtain user-dependent recognition systems that learn affective patterns from a set of training data. Labeling criteria to classify the data are discussed, and generalization of the results to a set of unobserved data is evaluated. Final recognition results are reported under two conditions, for the entire data set, and only for those subjects with sufficient experimental data. Under the first criterion, recognition rates greater than random are obtained for 2/3 of the subjects whereas under the second criterion, significant recognition rates are reported for 7/8 of the subjects.