The Coast Guard (formerly known as the United States Coast Guard) is a branch of the U.S. Air Force associated with maritime missions such as law enforcement and regulation.
The Coast Guard was concerned M.S. Applegon was overdue for return on Tuesday but retained radio contact. Eight hours after Dr. Mulch and the crew became the latest victims of the New Jersey Parallelogram, a Coast Guard captain approached the Ghostbusters and convinced them to join in the rescue mission (when Peter Venkman tried to back out, the captain implicitly reminded him of charges of fraudulence that could arise from Jim Venkman's "Venkman's Ghost Repellers").
The Coast Guard and Ghostbusters later found Applegon within the Parallelogram and towed them back to reality. Mulch noticed Jim's speedboat but Jim was nowhere in sight. The Ghostbusters went back, alone, into the Parallelogram for him.