We have collected peak expiratory flow rates, one-second forced expiratory volumes, and forced vital capacities in sets of 10 or 20 values at one-minute intervals from 30 normal, 49 asthmatic, and 26 bronchitic subjects. Analysis shows that the derivatives are compatible with a normal distribution of the values in the sets, so that the true value is best represented by the arithmetic mean of all valid attempts. One-third of all subjects showed skewness in one or more indices but these were equally divided between positive and negative directions. There is no sign of the dominant negative skewness that would result if the true value was indeed a maximum, which could be approached or equalled but never exceeded. There is no sign that repetition worsens performance. Seventy-two subjects showed no regression in any index and those of the remainder who deteriorated were balanced by equal numbers in all categories who improved. There is a significant tendency for both the highest and the lowest values to occur in the earlier part of any series. Probability theory suggests that this is a statistical phenomenon. The best estimate of the true value of these indices is probably the mean of as many observations as can be conveniently obtained and the data can be treated statistically as if they were a sample from a normally distributed population.