EVERYONE HAS relatives, and everyone has relatives he can't control. The First Brother, after all, was not Billy Carter but Cain. So an embarrassed nation has tended to offer its sympathy to Jimmy Carter over the past couple of years where his brother Billy's behavior was concerned, or, if incapable of sympathizing, it has at least averted its gaze. But the president cannot have it both ways -- dissociating himself from his brother's truly disgusting conduct in cozying up to Libya's terrorist-in-chief Muammar Qaddafi and -- at the same time -- permitting that brother to have the run of the White House and various agencies of government.

From just about day one of this administration (an administration, incidentally, whose leader made a big deal out of wanting to toughen up conflict-of-interest laws so that no one could profit from an association with the Carter government), Billy Carter has been profiting from his association, exploiting it for cash. For reasons that have always escaped us, this used to be chuckled over and, thereby, both sanctioned and encouraged. Billy Carter could command extravagant fees for appearing dressed up like a lunatic or doing some stunt or giving what his patrons were pleased to call a "speech." When the Libyan connection emerged, however, we were all assured by the White House that Billy's activities were 1) his affair solely, 2) beyond the reach of his brother, the president, and 3) in any event, wholly unrelated to U.S. government concerns.

Naturally Billy Carter, whose celebrity and the gifts that flowed from it depended on his patrons' belief in his importance, continued to exploit the connection. And naturally it was important to that connection that his Libyan patrons continue to believe in the connection's special power. How could the president, then, not have sawed off the relationship Billy Carter was so assiduously promoting and abusing? What is this, anyway, that we now read about how Billy was briefed by this one before his trip abroad and called and went to see that one and was granted an appointment with the other one, how he encountered his brother, the president, one recent day at the White House tennis courts, how the White House recommended a lawyer to him etc., etc., etc? Is it even possible that, on the lookout for someone who could engage their efforts in behalf of the American hostages last fall, Dr. Brzezinski could think only -- or even at all -- of Billy Carter? Does he, does Mr. Carter's White House, not know of the existence of any number of reliable and serviceable Americans here in town who could have pressed that button for them if requested?

The president cannot control his brother -- granted. But he could have long since informed the White House and agency staff who work for him that brother Billy was not to be received or involved in public affairs or treated any differently from Joe Doakes. And that is the point. Mr. Carter, after all, has not been unaware of the way many people in this country and around the world tend to view members of a president's family as official extensions of the presidency. In fact, in our judgement, he has rather overdone this idea himself, dispatching relatives as agents and emissaries where a duly elected or appointed official might have been more fitting. So he cannot have been oblivious of the connection from which his brother was profiting, even though the president had himself formally disavowed it. What remains incomprehensible is why Mr. Carter after all the warnings and embarrassments continued to let brother Billy have the run of the official barnyard.