The performance of the F test in identifying the correct number of components in exponential functions is investigated by mathematical and computational techniques. Uncoupled systems can be most easily identified when the relaxation times are widely separated but the exponential functions encountered in pharrnacokinetics and biochemistry are linked in that the amplitudes and eigenvalues are not independent. In such systems correct model discrimination occurs as the relaxation times become closer together. The possibility of nonreal eigenvalues is emphasized and an enzyme kinetic model with this property is investigated.