The departure of Rep. Dick Cheney as the No. 2 person in the House Republican leadership is causing an ideological and generational struggle for succession in a minority that has been losing its top people.

Rep. Edward Madigan, R-Ill., a moderate counted among the party's pragmatists, on Monday formally entered the contest to replace Cheney as House minority whip, challenging conservative Rep. Newt Gingrich, R-Ga., who had announced Friday he would seek the post.Cheney was beginning the confirmation process Tuesday in his nomination to become President Bush's secretary of defense. An election for his successor as whip will likely come after Congress returns from its Eas-ter recess next month.

"The more rapidly we get through this the better," said Sen. Tim Wirth, D-Colo., a member of the Senate Armed Services Committee. "I would hope we could be done by week's end."

Cheney lacks former Texas Sen. John Tower's defense experience, but his background as former President Ford's White House chief of staff for 14 months and reputation as a compromiser places him in good standing.

A third lawmaker seen as a strong possibility to make the race - Rep. Jerry Lewis of California, chairman of the House Republican Conference - spent Monday telephoning colleagues and had not yet decided whether to run, said a spokesman. Ideologically, Lewis is seen as somewhere between Madigan and Gingrich.

The matchup brought to the surface a long-simmering identity crisis for the Republicans, who have been in the minority in the House for better than three decades.

Madigan represents the old guard, those who have carved out a role for Republicans through cooperation with the majority Democrats and by choosing their political fights carefully.

Gingrich, leader of a band of several dozen arch-conservatives, advocates confrontation over conciliation. He has been the chief accuser of House Speaker Jim Wright over alleged ethics violations, and vociferously condemns what he terms the Democrats' "welfare state" while advocating a "conservative opportunity society."

An aide said Gingrich, after a weekend of calling colleagues, had secured the support of more than 40 of the 175 House Republicans.

One lawmaker, Rep. Thomas Petri, R-Wis., predicted the situation could become "a real brouhaha," with the potential for a bruising, high-level game of musical chairs within the leadership.

The departure of Cheney, who as minority whip was the party's chief House vote-counter and Minority Leader Robert Michel's heir apparent, leaves a vacuum in the GOP's top ranks in the House and was seen as a setback for Republican efforts to regain majority status.

"Dick Cheney was a major figure in the House Republican Party," said Thomas Mann, a longtime Congress-watcher at the Brookings Institution. "He is a man who was able to keep the divisions between the older, somewhat more traditional Republicans and the younger guerrilla warriors from erupting into open warfare. It's a serious loss for House Republicans."

The loss of Cheney so soon after the departure of Rep. Trent Lott, R-Miss., the former whip who won election to the Senate last year, and Rep. Jack Kemp, R-N.Y., now secretary of Housing and Urban Development, underscores what some see as the hopelessness of being a House Republican.

"It points to the difficulty they have in retaining their most talented members when other opportunities present themselves," Mann said.

Lewis was seen as the favorite to succeed Cheney should he decide to seek the No. 2 post. But such a move would open up the conference chairman's job and trigger a secondary scramble to fill that post, possibly involving others in the leadership hierarchy such as Rep. Mickey Edwards, R-Okla., who is chairman of the GOP Policy Committee. The Republican Research Committee chairman, Rep. Duncan Hunter, R-Calif., might then be tempted to move up in the pecking order, as well.

Michel was said by GOP officials to want to avoid a nasty fight within the party. Most in the current crop of leaders have been in their posts only two months, and a full-scale shakeup could only delay organizing efforts.