We study interplanetary coronal mass ejections (ICMEs) measured by probes at different heliocentric distances (0.3–1 AU) to investigate the propagation of ICMEs in the inner heliosphere and determine how the generic features of ICMEs change with heliospheric distance. Using data from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER), Venus Express and ACE spacecraft, we analyze with the superposed epoch technique the profiles of ICME substructures, namely, the sheath and the magnetic ejecta. We determine that the median magnetic field magnitude in the sheath correlates well with ICME speeds at 1 AU, and we use this proxy to order the ICMEs at all spacecraft. We then investigate the typical ICME profiles for three categories equivalent to slow, intermediate, and fast ICMEs. Contrary to fast ICMEs, slow ICMEs have a weaker solar wind field at the front and a more symmetric magnetic field profile. We find the asymmetry to be less pronounced at Earth than at Mercury, indicating a relaxation taking place as ICMEs propagate. We also find that the magnetic field intensities in the wake region of the ICMEs do not go back to the pre‐ICME solar wind intensities, suggesting that the effects of ICMEs on the ambient solar wind last longer than the duration of the transient event. Such results provide an indication of physical processes that need to be reproduced by numerical simulations of ICME propagation. The samples studied here will be greatly improved by future missions dedicated to the exploration of the inner heliosphere, such as Parker Solar Probe and Solar Orbiter.