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CCD images of the peculiar eclipsing binary V361 Lyrae were taken on five nights in June, 1993 at Kitt Peak National Observatory. Four new precision epochs of minimum light were determined and improved linear and quadratic ephemerides were calculated from all available epochs. The data indicate that the period of the system is continuously decreasing. We believe this is due to a gas stream leaving the L1 point of the primary component, striking directly the surface of the secondary component with a mass transfer rate of dM/dt $\sim$ 8(1) x 10$^-7$ solar mass/yr. The light curves are severely distorted, especially near phase 0.375. A parameter search using the simplex algorithm has been performed. Wilson-Devinney synthetic light curves using Kurucz model atmospheres were calculated. The system is semi-detatched, with the more massive component filling its Roche lobe and the secondary in a near-contact state. An 8800 K superluminous region was modelled on the secondary component. In other respects, the system consists of two fairly normal K dwarfs with a photometrically determined mass ratio $\sim$ 0.9. A substantial temperature difference between the components of $\sim$ 1000 K was determined. It is possible that V361 Lyrae allows us the unprecedented opportunity to study the formation of a typical W UMa contact binary.
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