It is a running Texas duel on Capitol Hill.

Two Republicans, both Texans, both conservatives, are on opposite sides of issues ranging from how to deal with sex offenders to what to do with stem cells. With so much in common, why are these people quarreling?

At a high-noon news conference, Sen. Kay Bailey Hutchison urged the House to pass her "Amber Alert" child-protection legislation without changes. Two hours later, House Majority Leader Tom DeLay, retorted that her bill would accomplish little without the House version's crackdown on sex offenders.

"This is what politicians do, they all want to be king of the hill," said Larry Sabato, director of the University of Virginia Center for Politics. "DeLay is majority leader and wants to run things from a Texas perspective as much as he can while a Texan is president. Hutchison has enough seniority now she's become prominent within the Senate."

Hutchison and DeLay have tangled over converting airport screeners to federal employees, spending federal money for light rail in Houston, increasing federal disaster assistance money and pulling the plug on Amtrak. They disagree on a woman's right to abortion and embryonic stem cell research.

Observers say the lawmakers' brands of conservatism, legislative style, job roles and their backgrounds feed the conflicts.

"They are different kinds of people, from different areas of Texas politics and they come out of different traditions," said Cal Jillian, political science professor at Southern Methodist University in Dallas.

DeLay, from a town outside Houston, was first in his family to go to college, while Hutchison circulates easily among the elite, Jillian said.

Hutchison, of Dallas, said she agrees with DeLay more than she disagrees, and she differs with him about as much as she does with any other lawmaker.

"I think we have the same general philosophy; we just have a different approach on certain issues where we've had disagreements, but they've always been in an agreeable way," Hutchison said in a recent interview.

DeLay was unavailable for comment. Spokesman Jonathan Grille said the two "may have an ideological distinction, even if its a slight one, but perhaps its an institutional distinction as well."

Hutchison and DeLay both have stood steadfast behind Bush on Iraq. Both support his tax cut plans and both have been allies in fights for federal spending on Johnson Space Center.

But when they differ, the opposition can be intense.

Hutchison pushed for improved airport security long before the Sept. 11 attacks, but that made her adamant about converting airport screeners to federal employees. DeLay argued hard for screening by private contractors under government oversight.

DeLay is responsible for a ban on spending federal money to build light rail in Houston, while Hutchison has pressed hard to win money for it.

Hutchison voted for the Senate's bill banning a procedure that opponents call partial-birth abortion. But she also backed a resolution affirming the Supreme Court's Roe vs. Wade ruling upholding a woman's right to an abortion.

DeLay is an unswerving opponent of abortion and has made a ban on partial-birth abortion a priority on the House agenda.

People who know them say DeLay and Hutchison, while not close, have a friendly relationship, but not the sort that Lyndon B. Johnson shared with fellow Texan Sam Rayburn when Johnson was a senator and Rayburn the House speaker.

"DeLay is deeply conservative in almost every respect. Hutchison is ... conservative on most issues, but she has a moderate streak. That's what irritates DeLay," Virginia's Sabato said.

Their differing styles and brands of conservatism work at the ballot box. In 2000, Hutchison won a third, six-year term with 65 percent of the statewide vote. DeLay won his 10th two-year House term last year with 63 percent of the vote in his suburban Houston district.