We developed a technique to continuously (i.e., automatically) monitor cardiac output (CO) and left atrial pressure (LAP) by mathematical analysis of the pulmonary artery pressure (PAP) waveform. The technique is unique to the few, previous related techniques in that it jointly estimates the two hemodynamic variables and analyzes the PAP waveform over time scales greater than a cardiac cycle wherein wave reflections and inertial effects cease to be major factors. First, a 6-min PAP waveform segment is analyzed so as to determine the pure exponential decay and equilibrium pressure that would eventually result if cardiac activity suddenly ceased (i.e., after the confounding wave reflections and inertial effects vanish). Then, the time constant of this exponential decay is computed and assumed to be proportional to the average pulmonary arterial resistance according to a Windkessel model, while the equilibrium pressure is regarded as average LAP. Finally, average proportional CO is determined similar to invoking Ohm's law and readily calibrated with one thermodilution measurement. To evaluate the technique, we performed experiments in five dogs in which the PAP waveform and accurate, but highly invasive, aortic flow probe CO and LAP catheter measurements were simultaneously recorded during common hemodynamic interventions. Our results showed overall calibrated CO and absolute LAP root-mean-squared-errors of 15.2% and 1.7 mmHg, respectively. For comparison, the root-mean-squared-error of classic end-diastolic PAP estimates of LAP was 4.7 mmHg. Upon future successful human testing, the technique may potentially be employed for continuous hemodynamic monitoring in critically ill patients with pulmonary artery catheters.