Temperature dependent X-ray photoemission spectroscopy (ESCA or XPS) studies on the Ta 4f lines in lT-TaS2, lT-TaSe2, lT-Ta0.97Hf0.03S2 and 2H-TaSe2 are reported. Striking effects arising from charge density waves (CDWs) are observed at low temperature. While electron diffraction evaluates the periodicity and direction of the CDWs, these XPS observations allow the different configurations of the CDWs with respect to the crystal lattice to be deduced. The results indicate the existence of CDW fluctuations in commensurate phases, and that in some incommensurate and ‘ quasi-commensurate ’ phases the CDWs cannot maintain long-range coherence. In lT-Ta0.97Hf0.03S2 and 2H-TaSe2 the Hf impurities pin the incommensurate CDWs into domains. © 1976, Taylor & Francis Group, LLC. All rights reserved.