In Turin on 29 September 1781 (by proxy) and again in Dresden on 24 October 1781 (in person), Anton married firstly with the Princess Caroline of Savoy (Maria Carolina Antonietta Adelaida), daughter of the King Victor Amadeus III of Sardinia and Maria Antonietta of Spain.
The Electress gave birth for last time in 1799 to another stillborn child.