It is demonstrated that the compounds of late actinides, namely Lawrencium and Nobelium surprisingly exhibit unusual nonactinide properties in that unlike other actinides the chemistry of these species is principally determined by the 7s and 7p orbitals rather than the 5f or 6d shells. Relativistic computations including electron correlation and spin-orbit effects using the complete-active space multiconfiguration self-consistent field followed by second-order and multireference relativistic configuration interaction (RCI) techniques are considered for the Lawrencium and Nobelium dihydrides as well the atoms. The ground and first excited states of Lawrencium and Nobelium arise from the 7s and 7p shells, and thus the potential energy surfaces of these species are unusual in having considerable 7p characteristics. Both molecules form stable bent ground states reminiscent of sp(2) hybridization with equilibrium bond angles near 120degrees. The Lawrencium compounds exhibit unusual characteristics due to avoided crossings of the potential energy surfaces. As a result of spin-orbit coupling, the B-2(2) state of LrH2 undergoes avoided crossing with the (2)A(1) state in the spin double group, which reduces the barrier for insertion of Lr into H-2. The Nobelium compounds are shown to be considerably less stable compared to Lawrencium compounds due to the relativistic stabilization of the 7s shell of the Nobelium atom. It is shown that the barrier for insertion of Lr into H-2 is lowered by relativity (spin-orbit coupling), while No has to surpass a larger barrier due to the relativistic stabilization of the 7s(2) shell, which is not very reactive. Lawrencium is the only element in the actinide series with unusually low ionization potential, and NoH2 has an unusually large dipole moment of 5.9 Debye. It is suggested that the Lawrencium and Nobelium compounds should have periodic similarities to the thallium and radium compounds, respectively.