The main goals of the paper are towards an understanding of the delay process in best-effort Internet for both non-congested and congested networks. A dedicated measurement system is re-ported for delay measurements in IP routers, which follows specifications of the IETF RFC 2679. The system is using both passive measurements and active probing. Dedicated application-layer software is used to generate UDP traffic with TCP-like characteristics. Pareto traffic models are used to generate self-similar traffic in the link. The reported results are in the form of several impor-tant statistics regarding processing delay of a router, router delay for a single data flow, router delay for more data flows as well as end-to-end delay for a chain of routers. We confirm results reported earlier about the fact that the delay in IP routers is generally influenced by traffic characteristics, link conditions and, at some extent, details in hardware implementation and different IOS releases. The delay in IP routers usually shows heavy-tailed characteristics. It may also occasionally show extreme values, which are due to improper functioning of the routers.