We present an analysis of archival Chandra and XMM-Newton observations of the magnetically-active cataclysmic variable DQ Her and the shell around it ejected in a nova event in 1934 . A careful revision of the Chandra observations confirms previous claims on the presence of extended X-ray emission around DQ Her and reveals that it actually corresponds to a bipolar jet-like structure extending \simeq 32 ^ { \prime \prime } along a direction from NE to SW . Therefore , this X-ray emission extends beyond the optical nova shell and is perpendicular to its major axis . The XMM-Newton observations confirm the presence of the extended X-ray emission detected by Chandra , suggesting the additional presence of a diffuse X-ray emission from a hot bubble filling the nova shell . This hot bubble was very likely produced by the explosion that created the nebular shell detected in optical images . The bipolar feature can be modelled by the combination of an optically thin plasma emission component with temperature T \approx 2 \times 10 ^ { 6 } K and a power law component with a photon index of \Gamma = 1.1 \pm 0.9 . Its X-ray luminosity in the 0.3–5 keV energy range is L _ { \mathrm { X } } = ( 2.1 \pm 1.3 ) \times 10 ^ { 29 } erg s ^ { -1 } , for an electron density n _ { \mathrm { e } } \approx 2 cm ^ { -3 } and a mass m _ { \mathrm { X } } \approx 3 \times 10 ^ { -6 } M _ { \odot } . We suggest that the X-ray bipolar structure in DQ Her is a jet and interpret its non-thermal X-ray emission in terms of a magnetized jet .