Fully relativistic four-component self-consistent field and correlated calculations at the Moller-Plesset second-order perturbation theory level (MP2) have been performed for the monofluorides and mono- and trihydrides of lanthanum, lutetium, actinium, and lawrencium. The calculated spectroscopic constants are in good agreement with available experimental data. The calculated bond lengths have been compared with values from nonrelativistic calculations to give an estimate of the effect of relativity on the molecular lanthanide and actinide contraction. The calculated lanthanide contraction at the relativistic MP2 level is 0.12, 0.12, and 0.19 Angstrom for the monohydrides, monofluorides, and trihydrides, respectively. The corresponding results for the actinides are 0.20, 0.15, and 0.28 Angstrom, and we demonstrate that the larger size of the actinide contraction is a consequence of relativistic effects. Between 10% and 30% of the lanthanide contraction and between 40% and 50% of the actinide contraction is caused by relativity in these compounds.