We report a detailed study of tunneling spectra measured on 2H-TaxNb1−xSe2 (x = 0 ∼ 0.1) single crystals using a low-temperature scanning tunneling microscope. The prominent gap-like feature unintelligible for a long time was found to be accompanied by some "in-gap" fine structures. By investigating the second-derivative spectra and their temperature and magnetic field dependencies, we were able to prove that inelastic electron tunneling is the origin of these features and obtain the Eliashberg function of 2H-TaxNb1−xSe2 at atomic scale, providing a potential way to study the local Eliashberg function and phonon spectra of the related transition-metal dichalcogenides.As a prototype of transition-metal dichalcogenides (TMDs), 2H-NbSe 2 keeps attracting great interest since it provides a platform, both in bulk and in its twodimensional form, to study the mechanism of chargedensity waves (CDWs) [1][2][3], interplay between CDWs and superconductivity (SC) [4][5][6], potential applications in electronic devices [7][8][9], and so on. In recent years, there is growing consensus that it is the wave-vectordependent strong electron-phonon coupling (EPC) that drives CDW formation [10][11][12]. However, unlike the typical strong EPC system of Pb [13], no characteristics of the tunneling spectra of 2H-NbSe 2 have been identified as its EPC function, i.e., the Eliashberg function. The dominant low-energy feature other than the superconducting gap is the kinks at approximately ±35 mV, which has been observed repeatedly by scanning tunneling microscopy/spectroscopy (STM/STS) [14,15]. This well-known gap-like feature was initially regarded as the CDW gap [14], but has not been demonstrated by subsequent measurements of angle-resolved photoelectron spectroscopy (ARPES) [16,17]. A recent STM/STS experiment ascribed it to the combination of a 35-mV electron self-energy effect and a non-symmetric CDW gap of approximately 12 meV [15], which is supported by the later ARPES experiment [5]. Nonetheless, it is confusing to note that no other phonon modes have been noticed by STS, although various modes in addition to the 35-meV one can be observed in the energy-momentum dispersions from ARPES [18].In this work, we performed precise STM/STS measurements for 2H-Ta x Nb 1−x Se 2 single crystals. In addition to the 35-mV gap-like feature, a series of "in-gap" shoulders/steps were observed in all samples. By investigating the second-derivative spectra of d 2 I/dV 2 and its temperature and magnetic field evolutions, we demonstrated that these spectroscopic features, including the long-term incomprehensible 35-mV enigma, originate from the inelastic electron tunneling process instead of a CDW gap [14] or the electron self-energy effect [15]. Meanwhile, a double Fermi-Dirac broadening effect was found to be a convenient way to distinguish an inelastic electron tunneling process. Then, the real-space resolved Eliashberg functions were obtained from inelastic electron tunneling spectroscopy (IETS), which might be extended to the study of other memb...