Trevor A. Hampton, who surprised Alexandria last month by resigning as the city's police chief a week after he was hired, was named the top police official in Durham, N.C., yesterday.

Also yesterday, signaling continued trouble in Alexandria's search for a new chief, city officials said they have placed a third round of advertisements soliciting applications. The new ads offer a higher salary and less stringent requirements for the post, which City Manager Vola Lawson has been trying to fill since last summer.

Hampton's selection in Durham was announced by City Manager Orville Powell, who called Hampton an "excellent, well-qualified" person to lead that city's law enforcement efforts. However, Powell acknowledged that he "agonized" over hiring Hampton, who is deputy police chief in Columbia, S.C., because of events in Alexandria.

On Jan. 21, Hampton attended a news conference in Alexandria and was symbolically awarded the gold shield of the police chief. He announced that he would begin work March 1.

The next week, however, without telling Alexandria officials, he agreed to interview for the job in Durham. After Alexandria officials learned that he was still seeking the Durham post, Hampton withdrew from the Alexandria job.

Hampton said his change of heart about Alexandria was largely because of his wife, a South Carolina native who decided after seeing Alexandria that she did not want to live there. Powell and Hampton have said that Hampton had not been promised the Durham job when he withdrew from the Alexandria position.

"He had no inside track or promises on this end," Powell said yesterday. In addition, Hampton told a news conference in Durham that "I had to make the Virginia decision on the basis that I would not get the Durham job. This was a family decision. We would have preferred to stay in South Carolina rather than going to Alexandria."

Lawson declined to comment on Hampton's hiring in Durham, but city officials have privately questioned whether Hampton was not assured of the Durham position when he dropped the Alexandria job.

One member of the Durham City Council had said publicly that the city would like to hire a black as police chief. Hampton was the only black among the six finalists for the Durham job.

Hampton will start work in Durham March 1 and will be paid $58,600 a year. His salary in Alexandria would have been $65,474.

The new advertisements for the Alexandria chief's job set a maximum salary of $72,184, up from the salary Hampton was offered. The ads also say that "strong preference" will be given to candidates who are police chiefs or deputy chiefs in cities of more than 50,000 population. Previous ads set those standards as absolute minimums. The city had hoped that a third round of ads would not be necessary and a chief could be found from among the earlier applicants.

The Alexandria Police Department has been without a permanent chief since Charles T. Strobel retired under pressure in September after his management was criticized.