Councilman Oden Barrett said Cleveland had indicated to him several times that he had problems working with Mayor Earnest Sparks.
"There's no working with the man," Barrett said Sunday afternoon of the mayor.
Another councilman, Glenville Twigg, said the police chief "has been indicating for quite some time that there were problems between him and the mayor."
Contacted Sunday night, Sparks said, "If Oden Barrett and his political cronies didn't seize this opportunity to score some political points, I'd be surprised.
"For the most part, I believe the police chief was doing his job," Sparks said.
As for any problem between he and Cleveland, Sparks said, "I didn't perceive of there being one."
Cleveland's wife, Mary Ellen, said he was unavailable Sunday night.
"We're very sad to leave Martinsburg. We've made a lot of friends here," she said.
Wayne Cleveland became chief in August 1994, after 24 years with the Montgomery County Police Department. Hopewell is a community of about 25,000 people about 25 miles southeast of Richmond, Va.
Barrett, a former city police officer, claimed several city officials have resigned because of problems with the mayor. He said they included Cleveland's predecessor, Perry Smith, former city manager Phil Hertz and former acting city manager Sharon Flick.
"It's been a power struggle ... He wants to exert powers he really doesn't have," Barrett said.
He and Twigg both said the city charter calls for most of the governmental power to be in the hands of the council, not the mayor.
"I haven't fired anybody. Have I requested people to do their jobs? Yes," Sparks said.
He added that Barrett wasn't a councilman when Smith was chief and said Smith retired and did not resign.
"Phil Hertz made the statement that if I were re-elected, he would resign. I was elected on a Tuesday. He resigned on Wednesday. Were there some problems with him and I? Certainly," Sparks said.
Sparks said citizens come to him with problems because "they feel I'm responsible. Then I address them to the appropriate department heads."
Councilman George Karos said he didn't want to comment on any problems between the council, mayor and police chief. Like Barrett, Twigg and Sparks, however, he said the resignation comes as no surprise, because the chief had indicated several months back that he was seeking another job.
"I think it's a great loss to the community of Martinsburg and Berkeley County, really," Karos said.
"He's been respected by the whole community. I know he had the respect of all the council members," Karos said of Cleveland.
"I hate to lose the man because I know in my heart what he's done for the people of Centre Street," Barrett said of his neighborhood.
"It's a great loss. Wayne Cleveland is one of the best, if not the best, police chief Martinsburg has ever had," Twigg said.
"The police department of the city of Martinsburg is probably one of the best-equipped in the state of West Virginia and there's been a lot of support for the department," Sparks said.
According to Sparks and Barrett, it could take several months to fill the position. In the meantime, Sparks said Capt. Ted Anderson will be the acting police chief.
"We knew it was coming. It's unfortunate," said one officer who asked not to be named.
"I hate to see the man leave. It's a real shame the politics in this town drove him out of here," said another police department employee who declined to be named.