Observations are reported of 19 symbiotic stars made with the imaging proportional counter of the Einstein Observatory. Three of the objects (HM Sge, V 1016 Cyg and RR Tel) were detected as soft X-ray sources. All three have shown slow-nova eruptions in the past 40 years. The data are interpreted as support of a model for slow novae involving thermonuclear events on white dwarfs which accrete from M giant companions. Symbiotic stars in their steady state, not being detected X-ray sources, are presumed to be powered by the accretion process alone.