Nina Stroganova, 78, a Danish-born ballerina who was a founding member of American Ballet Theater and later a demanding but much-respected dance teacher. Miss Stroganova, whose name was originally Rigmor Strom, received her early training in her native Copenhagen. In 1937, she joined the Mordkin Ballet, a New York company that served as the nucleus of Ballet Theater, as American Ballet Theater was originally known. She danced with Ballet Theater from its debut in 1940 until 1942 and again during the 1954-55 season. Stroganova taught at several New York schools and had her own studio in recent years. She was known as a demanding and keenly observant teacher who brought warmth and enthusiasm to her classes. In New York City on Tuesday of leukemia.