Develop low-order mechanistic models accounting quantitatively for, and identifiable from, the capnogram -the CO2 concentration in exhaled breath, recorded over time (Tcap) or exhaled volume (Vcap). Methods: The airflow model's single "alveolar" compartment has compliance and inertance, and feeds a resistive unperfused airway comprising a laminarflow region followed by a turbulent-mixing region. The gas-mixing model tracks mixing-region CO2 concentration, which is fitted breath-by-breath to the measured capnogram, yielding estimates of model parameters that characterize the capnogram. Results: For the 17 examined records (310 breaths) of airflow, airway pressure and Tcap from ventilated adult patients, the models fit closely (mean rmse 1% of end-tidal CO2 concentration on Vcap; 1.7% on Tcap). The associated parameters (4 for Vcap, 5 for Tcap) for each exhalation, and airflow parameters for the corresponding forced inhalation, are robustly estimated, and consonant with each other and literature values. The models also allow, using Tcap alone, estimation of the entire exhaled airflow waveform to within a scaling. This suggests new Tcap-based tests, analogous to spirometry but with normal breathing, for discriminating chronic obstructive pulmonary disease (COPD) from congestive heart failure (CHF). A version trained on 15 exhalations from each of 24 COPD/24 CHF Tcap records from one hospital, then tested 100 times with 15 random exhalations from each of 27 COPD/31 CHF Tcap records at another, gave mean accuracy 80.6% (stdev 2.1%). Another version, tested on 29 COPD/32 CHF, yielded AUROC 0.84. Conclusion: Our mechanistic models closely fit Tcap and Vcap measurements, and yield subject-specific parameter estimates. Significance: This can inform cardiorespiratory care.