At last count there were four bills being heard by Senate committees that are aimed at stifling relocation of sports franchises or granting other favors to the National Football League. When lumped together, they constitute as blatant an example of special-interest hanky-panky as ever befouled the halls of Congress.

The honorable senators who have leaped into the fray as if on signal from the NFL are not from all points of the congressional compass and hardly have the commonweal in mind. What they have in mind is cadging an advantage for cities in their four states that either are threatened with a loss of pro football franchises or hope to gain an expansion team.

So they are honeying up to the NFL with the introduction of all this legislation, each in its own way calculated to mightily please the lords of pro football. The noted aphorist Samuel Johnson would have understood their frenetic activity. It was he who said, "Self-interest is a busy prompter."

The petitioners are, in no special order of importance:

* Sens. Thomas Eagleton and John Danforth from Missouri, in which is located St. Louis, which has an NFL team named the Cardinals whose owners have been making unmistakable noises about leaving the town for dead as soon as the moment is propitious.

* Sen. Arlen Spector from Pennsylvania, as in Philadelphia, where Leonard Tose's dead-broke Eagles are still on an unsteady course and available to the first buyer who comes up with $60-$70 million to try to fetch the team out of state.

* Sen. Slade Gorton of Washington, where the Seattle Mariners have been something of a disaster, evoking goo-goo eyes from other cities passionate for major league baseball status.

* Sen. Dennis DeConcini, who is from Arizona, which just missed out on wangling the Eagles for Phoenix, and now wants to show the NFL it has no hard feelings but would like to help out in Congress, all of this with the next expansion franchise in mind.

The senators are trying to arrange a whole series of legislative gimmicks in their exercise of pitching woo to the big leagues. You want more control of who controls franchise movements? You got it. You want some exemptions from antitrust law? You got 'em. You want authority to pool cable and pay TV and other revenues? No problem, you got it.

To the NFL: you name it, you got it. Just don't let anybody steal our local teams, or, in Arizona's case, do put us in line quickly for an expansion franchise.

Mark Asher, the knowledgeable Washington Post reporter on the hearings scene, has capsuled the definitive purposes of each of the bills getting hearings. Perhaps the most fascinating is DeConcini's.

DeConcini is saying the intent of his bill is to deter franchise moves. This, only a few months after Phoenix was trying to steal the Eagles from Philadelphia, and thought it had them before being foiled. At that time, no hint of DeConcini's outrage against precipitate franchise shifts. Now he wants to play ball with the NFL, with a quid pro quo expansion team in mind, please.

Spector's bill would give a city, for example, Philadelphia, so many ways to protect a franchise that any out-of-state buyer would think 40 times before making an offer. The essence is that Philadelphia could match any offer for its Eagles. Spector calls his bill the Professional Football Stabilization Act, meaning, all you out-of-state guys lay off our team or the Professional Football Stabilization Act will eat you alive. A special feature of the Spector bill is that it is undisguised and the only one that isn't pandering to the NFL.

The Eagleton-Danforth bill, aimed at shooing away all bidders for the move-minded St. Louis Cardinals, who don't like local stadium conditions, butters up the NFL with a limited antitrust exemption for pro football and other sports.

And it sets forth 13 different barriers against a Cardinals franchise move, before the NFL could approve such a thing. Just in case that isn't enough protection for St. Louis, Eagleton and Danforth have a backup plan. They would have any move attempt also reviewed by a neutrally located U.S. District Court. Bidders, stay away from our Cardinals.

Gorton, in his bill, calls for an ad hoc Professional Sports Team Arbitration Board, as distinct from Spector's equally fancy-titled Professional Football Stabilization Act.

Gorton's bill doesn't make too much sense. It would let his board, whoever its members might be, decide all franchise shifts, but before his board decided anything, any request to relocate would be referred to the NFL, which would have to consider nine different, specified factors before making a preliminary judgment that could be overruled. How's that for going around the Horn?

And another thing: under the Gorton bill, pro football would have to add four teams by 1990, and major league baseball would have to expand by two franchises by 1988. That would give protection also to those foundering Mariners, whose franchise is coveted by more enthusiastic cities like Denver. Altogether, Gorton is looking out for his own.

Their strong home state interests are a stick-out feature of all the bills drafted by the honorable senators who, unabashedly, seem to have added the National Football League to their constituencies.