Measurements on insulating and conducting polymers from the polyaniline (PANI) family and investigations on semiconducting poly(tetrathiafulvalenes) (PTTF) have been used for illustration and discussion of some methodical questions of electron spin resonance (ESR). This concerns especially the new possibilities of the recently developed high-resolution ESR at the 2-mm waveband. it was applied for the study of the nature and dynamics of paramagnetic centres (PC) and charge carriers in PANI and PTTF. The rate of the quasi-one-dimensional (1D) intrachain electron motion and of the three-dimensional (3D) interchain electron hopping has been estimated separately. In iodine-doped PTTF the maximum electrical conductivity is 10^-4 S/cm. It is almost identical with the 3D-conductivity estimated by ESR and shows the typical temperature dependence of a semiconductor. The quasi-1D-conductivity is several orders of magnitude higher and shows in its dependence on temperature similarities with a metal. The PANI samples show in the highly doped form a maximum conductivity of about 10 S/cm and relatively small differences between the 1D- and 3D- conductivity, supporting the model of metallic islands