Senator Ted Stevens’s easy victory in Alaska’s Republican primary on Tuesday sets him up for two more fights this fall that are likely to be much tougher: one in the general election and the other in the courtroom.

The senator received 63 percent of the primary vote against six challengers, even as he faces a trial in September on charges that he concealed $250,000 in home renovations and gifts provided by an oil services company, VECO.

If the trial goes forward on schedule, Mr. Stevens, who has been in the Senate for 40 years and is revered in Alaska for bringing home billions of dollars in federal spending, will be defending himself in court while he also tries to hold off a strong general election challenge from a popular and well-financed Democrat, Mayor Mark Begich of Anchorage.

Mr. Begich led the senator by double digits in some polls before the primary, and he has received strong support from national Democrats who hope to strengthen the party’s Senate majority. Yet Mr. Stevens, who has long asserted that he alone has the seniority and effectiveness to keep projects coming to Alaska, is not expected to go down easily.