The asymptotic behavior of two Bernstein-Type operators is studied. In the first case, the rate of convergence of a Bernstein operator for a bounded founction \(f\) is studied at points \(x\) where \(f(x+)\) and \(f(x-)\) exist. In the second case, the rate of convergence of a Szász operator for a function of \(f\) whose derivative is of bounded variation is studied at points \(x\) where \(f(x+)\) and \(f(x-)\) exist. In the proof of the results some results in probability theory are used and some corresponding results are improved.