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This paper combines recent developments in the area of generation of dependent random variables with the advantages of the use of common and antithetic random numbers. This combination yields new efficient methods for estimating complicated stochastic quantities by simulation. Some theoretical and practical aspects of use of antithetic and common random numbers for variance reduction while using the total hazard construction are given. A proof of their optimality in estimating the expected value of the response sum or the response difference of functions of vector arguments with dependent components is presented. Some numerical examples illustrate the theory. (Author)