Apportionment of urban particulate matter (PM) to sources is central for air quality management and efficient reduction of the substantial public health risks associated with fine particles (PM(2.5)). Traffic is an important source combustion particles, but also a significant source of resuspended particles that chemically resemble Earth's crust and that are not affected by development of cleaner motor technologies. A substantial fraction of urban ambient PM originates from long-range transport outside the immediate urban environment including secondary particles formed from gaseous emissions of mainly sulphur, nitrogen oxides and ammonia. Most source apportionment studies are based on small number of fixed monitoring sites and capture well population exposures to regional and long-range transported particles. However, concentrations from local sources are very unevenly distributed and the results from such studies are therefore poorly representative of the actual exposures. The current study uses PM(2.5) data observed at population based random sampled residential locations in Athens, Basle and Helsinki with 17 elemental constituents, selected VOCs (xylenes, trimethylbenzenes, nonane and benzene) and light absorbance (black smoke). The major sources identified across the three cities included crustal, salt, long-range transported inorganic and traffic sources. Traffic was associated separately with source categories with crustal (especially Athens and Helsinki) and long-range transported chemical composition (all cities). Remarkably high fractions of the variability of elemental (R(2)>0.6 except for Ca in Basle 0.38) and chemical concentrations (R(2)>0.5 except benzene in Basle 0.22 and nonane in Athens 0.39) are explained by the source factors of an SEM model. The RAINS model that is currently used as the main tool in developing European air quality management policies seems to capture the local urban fraction (the city delta term) quite well, but underestimates crustal particle levels in the three cities of the current study. Utilizing structural equation modelling parallel with traditional principal component analysis (PCA) provides an objective method to determine the number of factors to be retained in a model and allows for formal hypotheses testing.