Very high-resolution (approximately 0.15 mas) VLBI hybrid maps of the two BL Lac objects Mkn421 and 0735 + 178 have been produced at lambda-1.35 cm. The structures of both sources are simple. Only an unresolved core is found in Mkn421. It is magnetic field dominated, and the motion of relativistic electrons is strongly restrained by the magnetic field. Relativistic electrons with relatively low energy are responsible for the synchrotron radiation. The maps of 0735 + 178 show that the radio structure at lambda-1.35 cm is dominated by a strong core, and there is a weak component outside. We can put a lower limit to the angular velocity of the outer component (0.32 +/- 0.03) mas yr-1, corresponding to an apparent transverse speed of (5.4 +/- 0.6)c which tallies with previous results. The outer component has an extension towards the south-east, a tendency also seen in the 6-cm VLBI maps. With our 1.35-cm VLBI observations, we demonstrate that it is possible to study a new component emerging from its core during an outburst and to study its behaviour on its way out.