This will work but It's error-prone. Better to borrow the idea used by \appendix:
\documentclass{report}
\newcommand{\annexname}{Annex}
\makeatletter
\newcommand\annex{\par
\setcounter{chapter}{0}%
\setcounter{section}{0}%
\gdef\@chapapp{\annexname}%
\gdef\thechapter{\@Roman\c@chapter}}
\makeatother
\begin{document}
\tableofcontents
\chapter{one}
\chapter{two}
\appendix
\chapter{one}
\chapter{two}
\annex
\chapter{one}
\chapter{two}
\end{document}
I have made Annexes numbered Roman (I, II, III, IV, etc) so that they don't conflict with Appendixes. If you're not using \appendix at all, you could simply change the meaning of \appendixname, and use \appendix instead:
\documentclass{report}
\renewcommand{\appendixname}{Annex}
\begin{document}
\tableofcontents
\chapter{one}
\chapter{two}
\appendix
\chapter{one}
\chapter{two}
\end{document}