Dr. Joseph Rosewater, 56, a Smithsonian Institution scientist and administrator since moving here in 1960 who was an authority on the classification and evolutionary biology of mollusks, died of cancer March 22 at the Washington Hospital Center. He lived in Rockville.

At the time of his death, Dr. Rosewater was curator of the mollusk division in the Smithsonian's National Museum of Natural History's department of invertebrate biology. In addition to his work at the Smithsonian, he was an adjunct professor at George Washington University's biology department, and had served on the dissertation committees of the University of Maryland, American University and the University of Delaware.

Dr. Rosewater was the author of more than 80 technical works, and had participated in field work with the International Indian Ocean Expedition. Field work had taken him to Indonesia, Panama, Malaysia, Bermuda, Cuba, Australia, and Ascension Island.

He was a past president of the American Malacological Union and the Biological Society of Washington. He had served on the governing board of the American Institute of Biological Sciences and was a member of the Conchologists of America.

Dr. Rosewater was a native of New Hampshire and earned bachelor's and master's degrees at the University of New Hampshire. He received his doctorate in biology from Harvard University. He served in the Army during the Korean conflict. He was an X-ray technician at a New Hampshire hospital and taught zoology at Mount St. Mary College in New Hampshire before moving here.

Survivors include his wife, Mary Carlson Rosewater, and a son, Carl Joseph, both of Rockville; two daughters, Katherine Rosewater of Sandown, N.H., and Gail Rosewater of Rockville, and a grandchild.