The relationships between peripheral blood pressure and blood volume pulse waveforms can provide valuable physiological data about the peripheral vascular system, and are the subject of this study. Blood pressure and volume pulse waveforms were collected from 12 normal male subjects using non-invasive optical techniques, finger arterial blood pressure (BP, Finapres: Datex-Ohmeda) and photoelectric plethysmography (PPG) respectively, and captured to computer for three equal (1 min) measurement phases: baseline, hand raising and hand elevated. This simple physiological challenge was designed to induce a significant drop in peripheral blood pressure. A simple first order lag transfer function was chosen to study the relationship between blood pressure (system input) and blood volume pulse waveforms (system output), with parameters describing the dynamics (time constant, tau) and input-output gain (K). tau and K were estimated for each subject using two different system identification techniques: a recursive parameter estimation algorithm which calculated tau and K from a linear auto-regressive with exogenous variable (ARX) model, and an artificial neural network which was trained to learn the non-linear process input-output relationships and then derive a linearized ARX model of the system. The identification techniques allowed the relationship between the blood pressure and blood volume pulses to be described simply, with the neural network technique providing a better model fit overall (p<0.05, Wilcoxon). The median falls in tau following the hand raise challenge were 26% and 31% for the linear and neural network based techniques respectively (both p<0.05, Wilcoxon). This preliminary study has shown that the time constant and gain parameters obtained using these techniques can provide physiological data for the clinical assessment of the peripheral circulation.