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Given the maxium size of any overshoot or under-shoot of the step response of a network whose system function is positive real, a lower bound on the rise time from zero to the final value is developed. Similarly lower bounds on the settling time are also derived. These results are improvements over previously published results. They are special cases of a general theorem which bounds the unit step response, A(t), for 0 Â¿ t < Â¿ when this response is bounded by (1Â±Â¿)r for t Â¿Â¿ where Â¿ is a positive real number and r is the final value of the unit step response.