During the War of the Second Coalition, Kospoth commanded a division in the reserve corps of the main army of Archduke Charles. He participated in the battles at Ostrach on 21. March 1799 and Stockach am 25. March 1799. Until May 1799 he commanded the Corps of Observation Villingen and in the Black Forest. At the storming of Mannheim on 18 September 1799, he commanded Archduke Charles' second column.