\documentclass{book}
\usepackage{appendix}
\begin{document}
\chapter{One} In Chapter One.
\section{First} In Section First.
\begin{subappendices}
\section{alpha} In Subappendix alpha
\subsection{alpha-one} In subsubappendix alpha-one
\section{beta} In Subppendix beta
\end{subappendices}  

\chapter{Two} In Chapter Two.
\section{First} In Section First.
\section{Second} In Section Second.
\begin{appendices}
\chapter{Alpha} In Appendix Alpha
\section{Alpha-One} In subappendix Alpha-One
\chapter{Beta} In Appendix Beta
\end{appendices}
\end{document}