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The occurrence and properties of Type Ia supernovae (SNe Ia) insingle-degenerate binary systems (white dwarf [WD] + nondegenerate companion)is examined for galaxies of different types, and as a function of redshift. Therates and characteristics (peak luminosities, expansion velocities of theejecta) expected from the explosion of mass-accreting WDs in symbiotic systemsand "helium star cataclysmics" are found to be different from those arising inanother class of candidate systems: cataclysmic-like (contact) systems (CLS),where a CO WD accretes hydrogen on a thermal time scale from a Roche-lobefilling main-sequence or subgiant companion. We derive the evolution of the SNeIa rate and properties resulting from the thermonuclear explosion ofsub-Chandrasekhar mass WDs in such systems when they detonate a helium layeraccumulated from steady burning of hydrogen at the surface. A fraction of CLSare believed to form a subset of the observed luminous supersoft X-ray sources(SSS). Sub-Chandrasekhar explosions from CLS are disfavored in all types ofgalaxies at redshifts z > 1. On the other hand, CLS where the WD succeeds togrow to the Chandrasekhar mass are more likely found in spiral galaxies, andabsent from early-type galaxies. SNe Ia statistics could (if the uncertaintiesstill involved are reduced) help to discriminate among proposed SNe Iascenarios. The range of variation of the characteristics of SNe Ia in the CLSscenario should be narrower than in symbiotics. The predicted correlationbetween peak luminosity and expansion velociy of the ejecta in SNe Ia comingfrom these systems is weak. For CLS, the distinction between thecharacteristics of SNe Ia respectively arising from sub-Chandrasekhar and fromChandrasekhar-mass explosions should be sharp, since all sub-ChandrasekharComment: uuencoded gz-compressed .tar PostScript file containing 16 pages and  2 figures, to appear in ApJ (Letters), Jan. 10, 199

The Single-Degenerate Scenario for Type Ia Supernovae in Cosmic Perspective