This paper is concerned with the estimation of parameters when mathematical models are fitted to data. Two new algorithms are presented. The first is fast (economical in computation time), requires no initial estimates, but is not so accurate. The second requires more computation time, and fairly accurate initial estimates, but achieves high accuracy. The models discussed consist of sets of coupled, non-linear differential equations, but the second algorithm is applicable to wider classes of models as well.The accuracy of the computed values of the parameters depends on the number of data points, and the errors in the data. The sensitivity of the different parameters to errors may differ by orders of magnitude. A method of calculating the expected errors in the parameters is described, and the results of some applications of the method are presented.