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(Abridged) We present results of several X-ray observations of the X-raybinary 4U 1954+31 performed with the satellites BeppoSAX, EXOSAT, ROSAT, RXTE,and Swift. We also studied the RXTE ASM data over a period of more than 10years. Light curves of all observations show an erratic behaviour with suddenincreases in the source emission on timescales variable from hundreds tothousands of seconds. There are no indications of changes in the sourcespectral hardness, with the possible exception of the RXTE pointed observation.Timing analysis does not reveal the presence of coherent pulsations orperiodicities either in the pointed observations in the range from 2 ms to 2000s or in the long-term RXTE ASM light curve on timescales from days to years.The 0.2-150 keV spectrum, obtained with BeppoSAX, is the widest for this sourceavailable to date in terms of spectral coverage and is well described by amodel consisting of a lower-energy thermal component (hot diffuse gas) plus ahigher-energy (Comptonization) emission, with the latter modified by apartially-covering cold absorber plus a warm (ionized) absorber. A blackbodymodelization of our BeppoSAX low-energy data is ruled out. The presence of acomplex absorber local to the source is also supported by the 0.1-2 keV ROSATspectrum. RXTE, EXOSAT and Swift X-ray spectroscopy is consistent with theabove results, but indicates variations in the density and the ionization ofthe local absorber. A 6.5 keV emission line is possibly detected in theBeppoSAX and RXTE spectra. All this information suggests that the scenario thatbetter describes 4U 1954+31 consists of a binary system in which a neutron starorbits in a highly inhomogeneus medium from a stellar wind coming from itsoptical companion, an M-type giant star.Comment: 13 pages, 5 figures (2 in the Appendix), 4 tables (1 in the  Appendix), accepted for publication on A&A, main journal. Revised version  includes the A&A Language Editor's correction

X-ray broad-band study of the symbiotic X-ray binary 4U 1954+31