The microstructure of the martensite structures in CuZr is investigated by conventional and high resolution electron microscopy. In Part I of these two sequential papers the details of the micro- and macrotwin arrangements are presented and discussed. The correlation between the microtwinning and the superstructure is confirmed and atomic models for twin interfaces, interface steps and twin tapering are derived. A comparison with earlier findings in the isostructural B19' NiTi martensite is made. The microtwins are (001) compound twins while the macrotwins are (021) Type I twins. A spear arrangement with a ((3) over bar 32) midrib is also observed. (C) 1998 Acta Metallurgica Inc.