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The actual theoretical research investigates the resonant high-energyspontaneous bremsstrahlung of ultrarelativistic electrons with considerableenergies in the field of a nucleus and a quasimonochromatic laser wave. Underthe resonant conditions within the laser field the intermediate virtualelectron transforms into the real particle. As a result, the accomplishedanalysis defines that the polar emission angle characterizes the frequency of aspontaneous photon. The study derives the expressions for the resonantdifferential cross-sections of the represented processes that realizesimultaneous registration of the frequency and radiation angle in correlationto the momentum of the initial electron (for the channel A) and of the finalelectron (for the channel B) of the spontaneous photon with absorption of $r$wave photons ($r = 1, 2, 3,... $ - the number of a resonance). Additionally,the distribution of the resonant differential cross-section as a function ofthe angle of the spontaneous photon emission for the higher numbers ofresonance ($r = 2, 3,... $) delineates a dependency with a sharp peak maximumthat coordinates to the particle radiation at the most probable frequency. Tosummarize, the accomplished work represents that the resonant differentialcross-section acquires considerable magnitude. Thus, for the first resonance ofthe channel A the resonant differential cross-section attains the $\sim10^{12}$ order of a magnitude, and for the third resonance of the channel B$\sim 10^5$ order of a magnitude (in the units of $\alpha Z^2 r_e^2$). Finally,numerous scientific facilities with specialization in pulsed laser radiation(SLAC, FAIR, XFEL, ELI, XCELS) may experimentally verify the constructed modelcalculations.

Resonant high-energy bremsstrahlung of ultrarelativistic electrons in the field of a nucleus and a pulsed light wave