In this paper the essential theoretical predictions for the nuclear muonic radioactivity are presented by using a special fission-like model similar with that used in description of the pionic emission during fission. Hence, a fission-like model for the muonic radioactivity takes into account the essential degree of freedom of the system: muon-fissility, muon-fission barrier height, etc. Using this model it was shown that most of the SHE-nuclei lie in the region where the muonic fissility parameters attain their limiting value X=1. Hence, the SHE-region is characterized by the absence of a classical barrier toward spontaneous muon and pion emissions. Numerical estimations on the yields for the natural muonic radioactivities of the transuranium elements as well numerical values for barrier heights are given only for even-even parent nuclei. Some experimental results from LCP-identification emission spectrum are reviewed. Also, the experimental results obtained by Khryachkov et al, using new spectrometer for investigation of ternary nuclear fission, are presented. The OPERA-experiment proposed to perform search for muonic radioactivity from lead nuclei, in the low background conditions offered by the Gran Sasso underground Laboratory (LNGS), is discussed.
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