High-resolution observations of 3C 129 and 3C 129.1 have been made at 2.7 GHz with the Cambridge 5-km telescope and 3C 129.1 is found to have a ‘bent-double’ structure. In 3C 129 there is no break in emission between the parent galaxy and the tail, suggesting that the supply of energy is continuous in time and is not from individual events. The linear polarization is coherent over individual regions of enhanced emission. In situ particle acceleration is required over most of the tail, even close to the galaxy, and the observations are consistent with the beam model for radio sources.