The invention pertains to a human or humanized anti-CD38 antibody or functional fragment thereof for use in a method of treating a tumor disease, in particular a haematological disease, by inducing specific killing of tumor cells that express CD38 by CD38 cross-linking. The antibody for use according to the invention include an antibody characterized by a variable heavy chain having the amino acid sequence of SEQ ID NO:6 and a variable light chain having the amino acid sequence of SEQ ID NO:14, an antibody characterized a variable heavy chain having the amino acid sequence of SEQ ID NO:5 and a variable light chain having the amino acid sequence of SEQ ID NO:13 as well as variants thereof.
