The methods comprise detection of gadolinium in human tissues and organs by refining the position of malignant neoplasm and radiation treatment of the neoplasm in order to damage its cells. Refined position of the malignant neoplasm is determined by introducing gadolinium into the patient body and scanning part of the patient body in which the neoplasm is located. The scanning is performed by displacement of zone of radiation concentration created by intersection of several X-ray beams having radiation energy corresponding to K-edge of gadolinium atoms absorption. The refined information is acquired using detectors sensitive to K.sub..alpha.-radiation of gadolinium atoms, to which secondary radiation is transported arising in zone of concentration. Scanning is performed of the region of the malignant neoplasm location utilizing the same means as in the first stage. Sources of X-ray radiation are switched with control means into elevated intensity mode, sufficient for radiation damage of the malignant neoplasm tissues.