The invention relates to curcumin derivatives having the formula I: wherein: Z represents: H3CO A represents —CH2—CH2— or —CH═CH— L represents —C(O)—(NH)n1—R—(NH)n2—C(O)— R represents a saturated or unsaturated, branched or unbranched hydrocarbyl chain having a minimum of 3 carbon atoms in the chain wherein the maximum number of carbon atoms in the chain is 24 and wherein the carbon atoms of the chain can be replaced by at least one heteroatom, wherein the heteroatoms are independently —O— or —NH2—, with the proviso that each heteroatom is separated from each other heteroatom by at least two carbon atoms n1 and n2 independently represent 0 or 1 and Y represents an antibody that binds specifically to a target antigen of a tumor cell. The invention further relates to methods of method of inhibiting the growth of tumors in a human by administering an effective amount of the curcumin derivative, and to methods of producing the curcumin derivative.