The nuclear level densities and level-density parameters in fissioning nuclei at their saddle points of fission barriers - $a_{f}$, as well as those for neutron - $a_{n}$, proton - $a_{p}$ , and $alpha$-particle - $a_{alpha}$ emission residues at the ground states are calculated for isotopic chains of superheavy nuclei with $Z$=112-120. The calculations are performed with the superfluid formalism using the single-particle energies obtained from the diagonalization of the deformed Woods-Saxon potential. Spectra were generated at global minima of the adiabatic potential energy surfaces, found by the multidimensional minimization method, and at the proper saddle points, found by the immersion water flow technique on multidimensional energy grids, with allowed the reflection and axial symmetry breaking. The influence of shell effects on the energy dependence of the ratios of level-density parameters corresponding to residues of the considered decay modes to those of neutron emission is studied. We have shown that, in contrast to the $a_{f}/a_{n}$ ratio, the $a_{p}/a_{n}$ and $a_{alpha}/a_{n}$ ratios do not show characteristic maxima depending on the excitation energy of the compound nucleus being formed. In the case of alpha decay, we identified the collective enhancement caused by cluster degrees of freedom to play quite an important role. The energetic course of the variability of the level density parameters before reaching the asymptotic value, not taken into account so far, will be of great importance for the estimation of the probabilities of de-excitation cascades via light particles emission in competition with splitting and thus for the determination of the survival probabilities and finally for the total production cross-sections of superheavy nuclei in channels with their (light particles) participation.
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