Rock glaciers and large ice‐debris complexes are common in many mountain ranges and are especially prominent in semi‐arid mountains such as the Andes or the Tien Shan. These features contain a significant amount of ice but their occurrence and evolution are not well known. Here, we present an inventory of the ice‐debris complexes for the Ak‐Shiirak, Tien Shan's second largest glacierised massif, and a holistic methodology to investigate two characteristic and large ice‐debris complexes in detail based on field investigations and remote sensing analysis using Sentinel‐1 SAR data, 1964 Corona and recent high resolution stereo images. Overall, we found 74 rock glaciers and ice‐debris complexes covering an area of 11.2 km2 (3.2% of the glacier coverage) with a mean elevation of about 3950 m asl. Most of the complexes are located south‐east of the main ridge of Ak‐Shiirak. Ground penetrating radar (GPR) measurements reveal high ice content with the occurrence of massif debris‐covered dead‐ice bodies in the parts within the Little Ice Age glacier extent. These parts showed significant surface lowering, in some places exceeding 20 m between 1964 and 2015. The periglacial parts are characterised by complex rock glaciers of different ages. These rock glaciers could be remnants of debris‐covered ice located in permafrost conditions. They show stable surface elevations with no or only very low surface movement. However, the characteristics of the fronts of most rock glacier parts indicate slight activity and elevation gains at the fronts slight advances. GPR data indicated less ice content and slanting layers which coincide with the ridges and furrows and could mainly be formed by glacier advances under permafrost conditions. Overall, the ice content is decreasing from the upper to the lower part of the ice‐debris complexes. Hence, these complexes, and especially the glacier‐affected parts, should be considered when assessing the hydrological impacts of climate change. © 2018 John Wiley & Sons, Ltd.