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The unusual supernova remnant CTB 80, containing the 39.5 millisecond pulsar PSR 1951+32, has been observed with the Position Sensitive Proportional Counter (PSPC) and the High Resolution Imager (HRI) on board the $\it{ROSAT}$ satellite. Morphological studies of CTB 80 in the radio energy band reveal a plerionic (i.e. center-filled) component and a shell-like component classifying CTB 80 as a composite-type SNR. Previous X-ray observations show a centrally located point source, coincident with the radio core and surrounded by diffuse emission. The $\it{ROSAT}$ observations allowed a clear detection of the pulsar, a compact nebula of $\sim$ 1~\am \ radius, and a diffuse nebula extended $\sim$ 5~\am \ eastward of the pulsar. All components were modelled with power law type spectra, with a range of acceptable column density and spectral index combinations. For the particular values of photon index $\Gamma$ $\sim$ 2 and an interstellar column density of N$_H \sim 3 \times 10^{21}$ cm$^{-2}$, the luminosities are $\sim \ 2.3 \ \times \ 10^{33} \ d_{2.5}^2$ ergs s$^{-1}$ from the point-like source, $\sim \ 3.9 \ \times \ 10^{33} \ d_{2.5}^2$ ergs s$^{-1}$ from the compact nebula, and $\sim \ 1.8 \ \times \ 10^{33} \ d_{2.5}^2$ ergs s$^{-1}$ from the 5\am \ diffuse nebula. The total combined luminosity represents $\geq$ 0.2 \% of the spin-down luminosity of the pulsar ($\dot{E}$ = 4 $\times$ 10$^{36}$ ergs s$^{-1}$). We have also detected pulsations from the 39.5 ms pulsar at the 99\% confidence level. The implied pulsed fraction is $\sim$ 35\% with a complicated energy-dependent behaviour. The full 2$^o$ $\times$ 2$^o$ PSPC image shows also a hard cone-like emission feature extending south-east of the pulsar out to the edge of the detector. The corresponding spectrum is best described by a two-temperature component Raymond-Smith thermal plasma with an average temperature of $\sim$ 10$^7$~K with an interstellar absorption column density of N$_H \sim 3 \times 10^{21}$ cm$^{-2}$. In the following, we present our $\it{ROSAT}$ analysis and discuss our results.
