Liquid-crystal elastomers (LCEs) are a class of actively moving polymers with remarkable practical potential for converting external stimuli into mechanical actuation. However, real-world applications of LCEs are lacking because macroscopic orientation of liquid-crystal order, which is required for reversible actuations, is hard to achieve in practice. Here we show that the processing bottleneck of LCEs can be overcome by introducing exchangeable links in place of permanent network crosslinks, a concept previously demonstrated for vitrimers. Liquid-crystal elastomers with exchangeable links (xLCEs) are mouldable, allow for easy processing and alignment, and can be subsequently altered through remoulding with different stress patterns, thus opening the way to practical xLCE actuators and artificial muscles. Surprisingly, instead of external-stress relaxation through the creep of non-liquid-crystal transient networks with exchangeable links, xLCEs develop strong liquid-crystal alignment as an alternative mechanism of mechanical relaxation.