Technical specifications for nuclear power plants limit both the annual quantity and the maximum release rate of activity to the environment. Demonstration of compliance, therefore, requires the measurement of long-term emissions as well as the capability of detecting changes in the release rate. At the same time, some effluents can only be monitored if they are concentrated on some sort of filter and the simplest way of satisfying both the sensitivity and response requirements is to use a monitor capable of continuous collecting and counting. In this paper, the ability of this type of monitor to perform the long and short term monitoring functions is analyzed. The long term emissions are shown to be directly related to the total number of counts obtained during the monitoring period. The short term function requires that the activity released be determined over short intervals. This results in significant statistical errors because the activity collected during the last interval has to be determined against a much larger background, consisting of the undecayed portion of all the activity previously collected. We have analyzed the statistical error resulting from this type of measurement for three methods of processing the data, including the commonly used differentiator circuit. The analysis shows that a method which is the digital analogue of the differentiator is preferred because it gives satisfactory statistical accuracy and it provides the greatest flexibility in the types of changes it can detect. The differentiator approach provides comparable statistical accuracy but is less flexible. A third method, in which the activity releases are determined for each separate interval, produces much poorer statistical accuracy than the other two.