  We study linear perturbations of Donoghue classes of scalar
Herglotz-Nevanlinna functions by a real parameter $Q$ and their representations
as impedance of conservative L-systems. Perturbation classes $\mathfrak M^Q$,
$\mathfrak M^Q_\kappa$, $\mathfrak M^{-1,Q}_\kappa$ are introduced and for each
class the realization theorem is stated and proved. We use a new approach that
leads to explicit new formulas describing the von Neumann parameter of the main
operator of a realizing L-system and the unimodular one corresponding to a
self-adjoint extension of the symmetric part of the main operator. The dynamics
of the presented formulas as functions of $Q$ is obtained. As a result, we
substantially enhance the existing realization theorem for scalar
Herglotz-Nevanlinna functions. In addition, we solve the inverse problem (with
uniqueness condition) of recovering the perturbed L-system knowing the
perturbation parameter $Q$ and the corresponding non-perturbed L-system.
Resolvent formulas describing the resolvents of main operators of perturbed
L-systems are presented. A concept of a unimodular transformation as well as
conditions of transformability of one perturbed L-system into another one are
discussed. Examples that illustrate the obtained results are presented.
