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The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfy λ0 = 0, λ j > 0 for each j > 0, and 
. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λ j = jλ, µj = jμ) with catastrophes of several different types.
