Summary: A domain \(R\) is called residually integrally closed if \(R/p\) is an integrally closed domain for each prime ideal \(p\) of \(R\). We show that residually integrally closed domains satisfy some chain conditions on prime ideals. We give characterization of such domains in case they contain a field of characteristic 0. Section 3 deals with domains \(R\) such that \(R/p\) is a unique factorization domain for each prime ideal \(p\) of \(R\), these domains are showed to be PID. We also prove that domains \(R\) such that \(R/p\) is a regular domain are exactly Dedekind domains.