The Cambridge 5-km radio telescope has been used to map the sources 3C 33, 6i .1, 379. 1 and 390.3 in both total intensity and linear polarization. The maps, which have a resolution of z".o arc in right ascension and z".o cosec in declination, reveal that the components of these sources contain features of high surface brightness, some of which show striking alignment with the associated optical objects. These features are in many cases highly polarized (up to 40 per cent) indicating that the scale of the magnetic field irregularities within them cannot be much smaller than the resolution of the telescope. The results of the observations are discussed in the light of the various theoretical models proposed to explain the existence of double extragalactic radio sources. it is concluded that the most tenable models are those in which energy is continuously transported to the components from the nucleus of the galaxy in the form of a beam of relativistic particles or low frequency waves.