The paper studies \(R\)-Carathéodory functions. The following characterization of an upper \(R\)-Carathéodory function is given: A function \(f\:T\times X\rightarrow R\) (\(T\) is a measurable space, \(X\) is a metrizable space) is upper \(R\)-Carathéodory iff \(f\) is the limit of a decreasing sequence of \(R\)-Carathéodory functions. A sandwich theorem for \(R\)-Carathéodory functions is proved. The proofs are based on the Marczewski function.