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Previous observations of the middle-aged $\gamma$-ray, X-ray, and radiopulsar B1055-52 indicated some peculiarities, such as a suspected changing ofthe X-ray flux and spectral parameters, a large excess of the alleged thermalcomponent of the ultraviolet (UV) spectrum over the Rayleigh-Jeans extension ofthe X-ray thermal spectrum, and a possible double break in the nonthermalspectral component between the optical and X-ray bands. We observed PSRB1055-52 with the XMM-Newton observatory in X-rays and the Hubble SpaceTelescope in near-infrared (NIR). The analysis of the XMM-Newton observationsdoes not support the notion of long-term changes in the X-ray flux andbroad-band X-ray spectrum of the pulsar. Using an observing mode less affectedby background noise than the previous XMM-Newton observations, we constrain thepower-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 datawe 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-raynonthermal spectra suggest that the NIR through X-ray emission can be describedby 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 theextension of the X-ray thermal component became smaller but did not disappear,indicating a non-uniformity of the bulk surface temperature. The NIR data alsoenable us to accurately measure the proper motion with values $\mu_\alpha=47.5\pm 0.7\,{\rm mas\,yr}^{-1}$ and $\mu_\delta = -8.7 \pm 0.7 \,{\rmmas\,yr}^{-1}$.

X-ray and near-infrared observations of the middle-aged pulsar B1055-52, its multiwavelength spectrum, and proper motion