We present the timing and spectral analyses of the XMM -Newton data on the 17-Myr-old , nearby radio pulsar B0950+08 . This observation revealed pulsations of the X-ray flux of PSR B0950+08 at its radio period , P \simeq 253 ms . The pulse shape and pulsed fraction are apparently different at lower and higher energies of the observed 0.2–10 keV energy range , which suggests that the radiation can not be explained by a single emission mechanism . The X-ray spectrum of the pulsar can be fitted with a power-law model with a photon index \Gamma = 1.75 \pm 0.15 and an ( isotropic ) luminosity L _ { X } = ( 9.8 \pm 0.2 ) \times 10 ^ { 29 } erg s ^ { -1 } in the 0.2–10 keV . Better fits are obtained with two-component , power-law plus thermal , models with \Gamma = 1.30 \pm 0.10 and L _ { X } = ( 9.7 \pm 0.1 ) \times 10 ^ { 29 } erg s ^ { -1 } for the power-law component that presumably originates from the pulsar ’ s magnetosphere . The thermal component , dominating at E \raisebox { -2.58 pt } { \mbox { $ \stackrel { < } { \mbox { \scriptsize$ \sim$ } } \ > $ } } 0.7 keV , can be interpreted as radiation from heated polar caps on the neutron star surface covered with a hydrogen atmosphere . The inferred effective temperature , radius , and bolometric luminosity of the polar caps are T _ { pc } \approx 1 MK , R _ { pc } \approx 250 m , and L _ { pc } \approx 3 \times 10 ^ { 29 } erg s ^ { -1 } . Optical through X-ray nonthermal spectrum of the pulsar can be described as a single power-law with \Gamma = 1.3 –1.4 for the two-component X-ray fit . The ratio of the nonthermal X-ray ( 1–10 keV ) luminosity to the nonthermal optical ( 4000–9000 Å ) luminosity , \approx 360 , is within the range of 10 ^ { 2 } – 10 ^ { 3 } observed for younger pulsars , which suggests that the magnetospheric X-ray and optical emissions are powered by the same mechanism in all pulsars , independent of age and spin-down power . Assuming a standard neutron star radius , the upper limit on the temperature of the bulk of the neutron star surface , inferred from the optical and X-ray data , is about 0.15 MK . We also analyze X-ray observations of several other old pulsars , B2224+65 , J2043+2740 , B0628–28 , B1813–36 , B1929+10 , and B0823+26 , and compare their properties with the those of PSR B0950+08 .