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We have studied for the first time the simultaneous generation of terahertz and X-ray radiation from noble gas based nano-cluster supersonic jet under "one-" and "two-color" (fundamental and its second harmonic) excitation with high-power femtosecond laser pulses. It was shown that optimal conditions for effective generation of terahertz and X-ray radiation are different, that makes possible efficient control by ratio between values of terahertz and X-ray signals generated simultaneously from gas based nano-cluster jet by means varying of time delay between laser pulse and cluster jet formation and by varying of laser pulse's chirp. It has been shown that efficiency of THz generation from cluster jet could be efficiently controlled by varying the ratio between clustered and buffer gases gas mixture; angular distribution of terahertz beam generated near by optical axis under "two-color" laser excitation conditions has been measured as well.