Much of his research includes testing evolutionary models in the fossil record, particularly the theory of punctuated equilibrium. His research is focused on the systematics and morphometrics of late Mesozoic and Cenozoicbryozoans found in deposits located in the Caribbean, especially the Dominican Republic, Panama, Costa Rica, and Venezuela, and the Gulf coast of the United States, particularly Florida, Alabama, and Mississippi. He has also worked extensively on Cenozoic bryozoans in England and southern Scandinavia and was a contributor to the Deep Sea Drilling Project on Cenozoic bryozoans recovered from the Atlantic and Pacific oceans. In April 1997 Cheetham was awarded the Raymond C. Moore Medal for Excellence in Paleontology by the Society for Sedimentary Geology. In November 2001 he received the Paleontological Society Medal; he was, during the same year, honored with a festschrift titled Evolutionary Patterns, edited by Jeremy Jackson, Scott Lidgard, and Frank McKinney.
He is married to the former Marjorie Rogers; they have four children and two grandchildren.