\documentclass{report}

\usepackage{multibib}
\newcites{one}{First references}

\begin{document}

\chapter{First chapter}

The answer to life the universe and everything is 42 \citeone{DouglasAdams}

\bibliographystyleone{plain}
\bibliographyone{bibliography}

\chapter{Second chapter}

All that glitters is not gold \cite{Tolkien}

\bibliographystyle{plain}
\bibliography{bibliography}

\end{document}

