The beam-foil method was used to determine mean-lives of excited atomic states. Initial studies were done on states. Initial studies were done on states of the helium- and hydrogen-like ions B IV and B V, with the mean-lives determined by fitting the decay curves to sums of exponential terms. Since theoretical values of the mean-lives are very precise in these simple atomic systems, our results indicate the accuracy of the experimental method. A series of measurements was made of the low lying 2s 2p⁴ states in nitrogen-like Ne IV, Na V, Mg VI, Al VII, and Si VIII. The experimental results were compared to theoretical calculations of Fawcett and Sinanoglu, and showed excellent agreement with Sinanolu's nonclosed-shell many electron theory. The lifetimes of the 4p ²P₁/₂ and 4p ²P₃/₂ states in copper-like Br VII were determined by measuring decay curves for both the primary and cascade decays and then analyzing the curves jointly. Our resulting mean-life values are considerbly shorter than those of previous experiments which analyzed only the primary decay curve. Comparison with theoretical calculations showed excellent agreement with those which include core polarization effects.