An electroactive sensing or actuating material comprises a composite made from a polymer with polarizable moieties and an effective amount of carbon nanotubes incorporated in the polymer for a predetermined electomechanical operation of the composite when such composite is affected by an external stimulus. In another embodiment, the composite comprises a third component of micro-sized to nano-sized particles of an electroactive ceramic that is also incorporated in the polymer matrix. The method for making the three-phase composite comprises either incorporating the carbon nanotubes in the polymer matrix before incorporation of the particles of ceramic or mixing the carbon nanotubes and particles of ceramic together in a solution before incorporation in the polymer matrix.