Abstract: The invention concerns a composition, i.e., a multifunctional medically active agent for rational therapy of malignant (cancerous) diseases based on cause-and-effect relationship. The new composition according to the invention contains dimethylsulfoxide, DMSO, or sulfolan, preferably DMSO, in combination with a therapeutically effective amount of at least one cytostatic agent. The invention also concerns a method for treatment of malignant (cancerous) conditions in man comprising local or systemic administration thereto of an effective dosage of the composition according to the invention.The invention surprisingly provides a composition, as well as a method of treatment, allowing rational specific or selective carcinostatic-carcinocidic therapy. This therapy-form aims at the intracytoplasmic 3-dimensional cytoskeleton (differentiation organelle) that is specifically changed in the malignant cells, as well as at the targets responsible for karyokinesis and cytokinesis.