  An analytic study is presented of the efficient multiphoton excitation and
strong harmonic generation in three-level systems specified by a pair of nearly
degenerate, strongly dipole-coupled excited states. Such systems are physically
formed by the three lowest states in, e.g., the hydrogen atom or evenly charged
homonuclear diatomic molecular ions under reasonably chosen laser intensities.
As a detailed analytic result, we found that the laser pulse of photon energy
$2{.}05\text{eV}$, duration $0{.}23\text{ps}$ and intensity $5\cdot
10^{13}\,\frac{\text{W}}{\text{cm}^2}$ is able to produce complete inversion of
the initial population in the hydrogen atom through the 5-photon excitation. At
the same photon energy, the pulse of duration $0{.}41\text{ps}$ and intensity
$3{.}44\cdot 10^{14}\,\frac{\text{W}}{\text{cm}^2}$ was found to produce the
same effect in the molecular ion but through the 9-photon excitation. We show
that the accompanying scattering of light has very rich spectrum differing
substantially from that of the two-level system.
