We describe a method and show the measurement results of the radioactive fallout samples collected in Shanghai area soon after the March 1978 nuclear test of China. These environmental samples which contain about 20 short-lived γ-emitting isotopes

have very weak radioactivity (10

-11

~10

-9

curies) . Two algorithms are used to determine the peak areas: the Wasson Algorithm (WA) for single peaks

and the nonlinear least-squares fitting algorithm without matrix inversion (AWMI) for unresolved peaks. It has been proved successful to apply this combined method to low-level

γ

ray spectrum assay.