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Quasiparticle band dispersion in the vicinity of the Fermi surface of quasi-two dimensional systems of two types has been studied in this thesis: layered transition metal dichalcogenides (TMDC) of the 1T-family and surface states in thin silver films on Au(111). Among TMDCs TaSe2, TaS2 and TiSe2 are charge density wave materials, while TiTe2 is a Fermi liquid reference compound. On Au(111) one observes surface state dispersion upon evaporation of 1-10 ML of silver. The common feature of these different systems is the anisotropy of the band-structure, revealing the quasi-two dimensional character of the initial states, which are investigated by photoelectron spectroscopy. This allows a straightforward interpretation of the photoemission spectra in terms of the mapping of initial bands of the crystal.