The counting of particles or radiation emitted during the radioactive decay of a sample of mixed radionuclides can be used in the determination of the numbers of atoms of individual isotopes present and hence their activities. If the isotopes emit different particles these may be counted in different counting systems and give additional information from which the activities can be determined. For a mixture of isotopes, methods using fixed counting times may be difficult to optimise. A method has been devised which calculates the best fit of the experimental total count to the theoretical total count, by using the numbers of atoms of each isotope present in the sample as the parameters of the fit. This method of time evolved least squares (TELS) uses the individual times of decay of the separate isotopes present. Thus the maximum information about the activities of the isotopes present is used. The method has previously been applied to the counting in a limited number of detectors for the evaluation of the descendants of radon. It is generalised to counting an arbitrary number of radioactive isotopes in any number of counters. The number of atoms of each isotope present may be determined in real time with allowance being made for different counter efficiencies and for the overlap of counting into different counters. The methodology is outlined and the general theory is derived. It is noted that the fitting of the theoretical and experimental total counts can proceed in real time and provide progressively updated estimates of the activities of the species present. A future paper will discuss the application of this method to the counting of samples of the descendants of radon.