The invention relates to selective new caspase-2 inhibitors that recognize caspase-2 and prevent and block its activity based on the following backbone: 2-Quinolinylcarbonyl-L-Valinyl-L-Aspartyl (methyl ester)-L-Valinyl-L-Alanyl-L-Aspartyl (methyl ester) 2,6-difluorophenyl ester SEQ ID NO:1) and derivatives thereof, SEQ ID NO:1 corresponding to formulae Ia or Ib. Application of the inhibitors for preventing and treating diseases involving caspase-2.