LaCu2 is the only compound among the RCu2 series (R from La to Lu, and Y) which crystallizes in the hexagonal AlB2-type structure, whereas the other compounds show the orthorhombic CeCu2-type structure. In agreement with ab initio calculations our high-pressure x-ray diffraction experiments show that LaCu2 transforms at relatively low pressures to the CeCu2-type structure, which can be regarded as a low-symmetry variant of the AlB2-type structure. To investigate the stability of the CeCu2-type structure we performed high-pressure x-ray diffraction experiments on YCu2 using argon as the pressure transmitting medium. These experiments showed in contrast to an earlier study that the CeCu2 structure is stable at least up to the highest attained pressure of 35 GPa. The tendency for amorphization at pressures above 10 GPa, as observed in the earlier study, was probably due to the non-hydrostatic conditions of the pressure transmitting medium, showing that the CeCu2-type compounds are very sensitive to non-hydrostatic compression. A transition to the MgCu2-type structure (cubic Laves phase) at about 28 GPa, as predicted by the ab initio calculations, has not been observed.