We have investigated the nature of magnetic ground state of RCrTiO5 (R = Dy and Ho) through dc magnetization and heat capacity measurements. Due to the strong competition between the Cr3+ and R3+ sublattice moments, several intriguing phenomena have been observed when the magnetic state is probed at low field. In both the systems, the Cr3+ sublattice undergoes a long-range antiferromagnetic ordering below ∼139 K with a weak ferromagnetic (FM) moment perpendicular to c axis as evident from the hysteresis in M(H) curve. At low fields (150 Oe), the zero-field-cooled magnetization shows that the FM component of Cr3+ spin and R3+ moments align in the opposite direction with respect to each other and the net moment aligns in the opposite direction to the applied field in the temperature range 136–16 K for DyCrTiO5 and below 128 K for HoCrTiO5. For both the samples, the strong coupling between the two magnetic sublattices is manifested in the temperature dependence of coercive field. Another interesting phenomenon, the spin reorientation transition, has been observed below K, where the easy axis of FM moment of Cr3+ starts to rotate from one crystallographic axis toward another in DyCrTiO5 but no such transition has been observed in HoCrTiO5. The other members of RCrTiO5 series do not show such kinds of interesting magnetic properties.