Data taken with ten Cosmic Ray Tracking (CRT) detectors and the HEGRA air-shower array on La Palma, Canary Islands, have been analysed to investigate changes of the cosmic overlineray mass composition at the 'knee' of the cosmic-ray flux spectrum near 10 15 eV energy. The analysis is based on the angular distributions of particles in air showers. HEGRA data provided the shower size, direction, and core position and CRT data the particle track information. It is shown that the angular distribution of muons in air showers is sensitive to the composition over a wide range of shower sizes and, thus, primary cosmic-ray energies with little systematic uncertainties. Results can be easily expressed in terms of <ln A> of primary cosmic rays. In the lower part of the energy range covered, we have considerable overlap with direct composition measurements by the JACEE collaboration and find compatible results in the observed rise of <ln A>. Above about 10 15 eV energy we find no or at most a slow further rise of <ln A>. Simple cosmic-ray composition models are presented which are fully consistent with our results as well as the JACEE flux and composition measurements and the flux measurements of the Tibet ASγ collaboration. Minimal three-parameter composition models defined by the same power-law slope of all elements below the knee and a common change in slope at a fixed rigidity are inconsistent with these data.