  We report the discovery of [NeV]3426 emission, in addition to HeII4686
emission, in six compact star-forming galaxies. These observations considerably
increase the sample of eight such galaxies discovered earlier by our group. For
four of the new galaxies, the optical observations are supplemented by
near-infrared spectra. All galaxies, but one, have HII regions that are dense,
with electron number densities of ~300-700 cm-3. They are all characterised by
high Hbeta equivalent widths EW(Hbeta)~190-520A and high
O32=[OIII]5007/[OII]3727 ratios of 10-30, indicating young starburst ages and
the presence of high ionization radiation. All are low-metallicity objects with
12+logO/H=7.46-7.88. The spectra of all galaxies show a low-intensity broad
component of the Halpha line and five out of six objects show Wolf-Rayet
features. Comparison with photoionization models shows that pure stellar
ionization radiation from massive stars is not hard enough to produce such
strong [NeV] and HeII emission in our galaxies. The [NeV]3426/HeII4686 flux
ratio of ~1.2 in J1222+3602 is consistent with some contribution of active
galactic nucleus ionizing radiation. However, in the remaining five galaxies,
this ratio is considerably lower, <0.4. The most plausible models are likely to
be non-uniform in density, where HeII and [NeV] lines are emitted in
low-density channels made by outflows and illuminated by harder ionizing
radiation from radiative shocks propagating through these channels, whereas
[OIII] emission originates in denser regions exposed to softer stellar ionizing
sources.
