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This paper presents results of investigations aimed at the creation of high-power explosive sources of soft X-ray radiation (SXR) for thermonuclear-target ignition. Successful tests of basic elements of the power system of such sources: a disk magnetocumulative generator of 480-mm diameter and explosive-current opening switch, have been carried out. These elements will provide current pulses of 50, ... , 70 MA amplitude at rise time of 0.5, ..., 1 μs. The technology aimed at generation of the SXR, powered from the explosive-current sources, is developed. SXR pulses of 55-ns length and energy of ~ 800 kJ have been recorded at a liner current of 14 MA with a rise time of 1 μs. Analysis of the experimental data is carried out using a 2-D MHD code. The most probable scenario of implosion of single and nested array liners is determined. A conclusion about the perspectives of the developed direction and its competitiveness with stationary facilities is made.