Measurements of the production of neutrons by negative μ mesons which stop and interact in two materials, sodium and magnesium, are reported. The mean number of neutrons emitted per interaction was found to be 0.6+/-0.2 for magnesium and 1.0+/-0.4 for sodium, where the uncertainties include an estimated contribution from systematic sources as well as those of a statistical nature. The data confirm that neutron production in magnesium is less than in lead (multiplicity 1.7+/-0.3), but show that it is not zero. Neutron production in sodium also is shown to be measurable and probably greater than in magnesium, though less than in lead. In the course of the experiment a value of (1.18+0.19-0.14) μsec (statistical) was found for the mean life of negative μ mesons in sodium.