  Previous observations of the middle-aged $\gamma$-ray, X-ray, and radio
pulsar B1055-52 indicated some peculiarities, such as a suspected changing of
the X-ray flux and spectral parameters, a large excess of the alleged thermal
component of the ultraviolet (UV) spectrum over the Rayleigh-Jeans extension of
the X-ray thermal spectrum, and a possible double break in the nonthermal
spectral component between the optical and X-ray bands. We observed PSR
B1055-52 with the XMM-Newton observatory in X-rays and the Hubble Space
Telescope in near-infrared (NIR). The analysis of the XMM-Newton observations
does not support the notion of long-term changes in the X-ray flux and
broad-band X-ray spectrum of the pulsar. Using an observing mode less affected
by background noise than the previous XMM-Newton observations, we constrain the
power-law (PL) spectral index as $\alpha_X=-0.57^{+0.26}_{-0.25} $ ($F_{\nu}
\propto \nu^{\alpha}$) in the energy band 3-10 keV. From the NIR-optical data
we obtain a PL slope $\alpha_O= -0.24 \pm 0.10$ for the color index
$E(B-V)=0.03$ mag. The slopes and fluxes of the NIR-optical and X-ray
nonthermal spectra suggest that the NIR through X-ray emission can be described
by the same PL and is generated by the same mechanism, unlike the pulsar's
$\gamma$-ray emission. The excess of the UV thermal component over the
extension of the X-ray thermal component became smaller but did not disappear,
indicating a non-uniformity of the bulk surface temperature. The NIR data also
enable us to accurately measure the proper motion with values $\mu_\alpha
=47.5\pm 0.7\,{\rm mas\,yr}^{-1}$ and $\mu_\delta = -8.7 \pm 0.7 \,{\rm
mas\,yr}^{-1}$.
