True triaxial short-term and long-term tests were conducted on three different types of hard rocks, namely, marble, basalt and granite. During true triaxial long-term creep tests, the crack evolution information was collected by using an acoustic emission system. The micro-structures before and after creep tests were analysed by scanning electron microscopy and polarising microscopy. The time-dependent propagation of cracks in hard rocks is affected by applied stress and the mineral composition. The high axial stress makes the cracks propagate with time development during creep stage. When the axial stress exceeds the damage stress, the AE signals intensity have increased significantly. The damage stress values determined through short-term and long-term tests are different, but the difference is small so that the former can be used efficiently to test the damage stress in terms of long-term strength analysis. Accumulation of extensile cracks induced by high applied axial stress eventually can cause creep failure of hard rocks; however, the time-effect seems to only increase the micro-cracking inside the rock. The ultimate macroscopic failure surface of the rock sample appears to only be affected by the difference between σ2 and σ3. The time-dependent dilatancy of Jinping marble and Baihetan basalt exceeded that of granite specimens. Under creep loading, calcite and pyroxene, which have lower hardness values, are more prone to crack time-dependent expansion than feldspar and quartz, which have higher hardness values.