Joint theory of gamma-generation (GO) and radiation-heat regime (GG&RH) in active medium (AM) of y-taser (GL) is applied for the analyses of total world experience in the CL-problem in order to choose those nuclei-candidates, active media, GL-schemes which are indeed actual for the GL-creation. The classification of CL over a degree of the womfortable conditions for the GG is given. The GLschemes could be rsidential(Rsd) (creation of excited laser-active nuclei, ELAN, from its parents directly in the site of AM) or nonresidential(Nrsd)' (creaon of ELAN out off the AM). It has been turned out that all residentiaI part of the wod experience does not fit for the realization of GL and can be considered only as a museum-piece. Any Rsd AM on the short-lived isomers must be inevitably blasted before the beginning of the GG. That Imuseuml part includes a lot of ideas: GG on long-lived isomers; line narrowing by radio-frequency or optical fields; creation of -y-gain in the inversionless mixture of the excited and dc-excited nuclei (amplification without inversion); super-dilution of work-nuclei in a matrix via multi wave Borrman effect; non-Moessbauer active media in plasma, gas or beam with its optical laser cooling, a lot of schemes (one-stage, two-stage, two-phase, two-step, two-photon, etc.). The exception could be only Rsd GL pumped by another CL. Butthe Nrsd part of wod expeence had stood yet all stricttests of that joint theory. (induced, super-radiant, in plasma, in beam, in solid); laser cooling of atomic beam; amplification without inversion; Borrmann effect; Shpolskii effect; Moessbauer effect; hyper fine structure; laser selection (separation) of excited nuclei, isomers, isotopes; radiation-heat regime of active media of gamma-laser anomalous superdilution DTRODIJCTION The most advanced non residential (Nrsd GL (see ABSTRACT) is based on the use of the short-lived isomers (1O -1O 5) produced under nuclear pulse radiation in a special converteruf28] (alias multibeam emitter, MBE [34][35][36]) and delivered into the AM by the method SPTEN (Soft Prompt Transplantaon of Excited Nuclei) with use of the complex of measures for well generation and cooling of AM[27-36}. The enriched bunch with 90% of the Excited Laser-Active Nuclei (ELAN) is delivered into the site of AM just before the GG. Hence the Nrsd GL could be characterized by the removal from the site of AM absolutely all processes for the nuclei activation and for the inverted population creation. Only the GG and the cooling are acting in such Nrsd AM. Hence the Nrsd GL could do without use of any methods for the creation of gain in the inversionless medium because the Nrsd AM is strongly inverted before its creation, at beam-study', out off the AMs site. Owing to such circumstance the ideas developed in works[2728-36} allow to obviate the most weak flows of the OL-schemes. One such weak flow was pointed in Refsf91O,12,32,35j. It may be any process or device based on use of the hyperfine structure (HFS) directly in the AM (/n s/tm. The ideas of works[27-36J d...