The use of series expansion methods in treating threshold-detector activation data has been analyzed. Normally the indiscriminate use of detectors having similar responses leads to unstable and ill-conditioned systems. The reasons for these deficiencies are determined and a new method for overcoming them is proposed. To make optimum use of the experimental data in obtaining a solution for the incident neutron spectrum, the series expansions coefficients are obtained through the Gauss method by solving a least-squares problem. A procedure, based on the Monte Carlo method, has been set up to statistically study the effect of experimental input errors on the solution obtained. The most important results indicate that: any set of threshold detectors can be used independent of their cross-section shapes the reliability increases as the number of detectors increases the reliability decreases when the number of series expansion terms increases.