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The ЗАЗ-968 Zaporozhets was produced from 1972 to 1980. Here is the charming ЗАЗ-968A, featuring a smaller engine and intended, it would seem, for the female driver.
Note: Since I wrote the above Mrs Kartoshka has informed me that the ЗАЗ-968 A was usually the car of older people, and that women drivers in the Soviet Union were not a common sight outside of Moscow and Leningrad.