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We introduce different ensembles of random Lindblad operators $\cal L$, which
satisfy quantum detailed balance condition with respect to the given stationary
state $\sigma$ of size $N$, and investigate their spectral properties. Such
operators are known as `Davies generators' and their eigenvalues are real;
however, their spectral densities depend on $\sigma$. We propose different
structured ensembles of random matrices, which allow us to tackle the problem
analytically in the extreme cases of Davies generators corresponding to random
$\sigma$ with a non-degenerate spectrum for the maximally mixed stationary
state, $\sigma = \mathbf{1} /N$. Interestingly, in the latter case the density
can be reasonably well approximated by integrating out the imaginary component
of the spectral density characteristic to the ensemble of random unconstrained
Lindblad operators. The case of asymptotic states with partially degenerated
spectra is also addressed. Finally, we demonstrate that similar universal
properties hold for the detailed balance-obeying Kolmogorov generators obtained
by applying superdecoherence to an ensemble of random Davies generators. In
this way we construct an ensemble of random classical generators with imposed
detailed balance condition.