The second month of the towboat pilot strike on inland waterways is starting with a test for towboat companies and a mystery.

The FBI is investigating a massive 137-barge breakup that took place near St. Louis two weeks ago. The breakup underlines the challenge to safety faced by towboat companies.The companies replaced pilots who walked out on April 3 with little or no disruption to crucial supplies of grain, petrochemicals and other goods on the Mississippi River and other inland waterways.

About 4,000 tugboats push barges of goods on the waterways. The Pilots Agree union says about 800 of its members are on strike.

The replacements, many of whom were called in during their rest period, are due to be relieved after their usual 30 days on the job. Companies say that is no problem, because so few members of the Pilots Agree union walked off over pay, working conditions and safety issues.

The union claims companies will have to either overwork the replacement pilots or bring in inexperienced pilots. Either action would be particularly dangerous on waterways swollen by spring rains.

''We feel it's crunch time,'' said Art Sasse, a spokesman for Pilots Agree. ''We are hopeful that, in the next week to 10 days, maybe some of the smaller companies that have been hardest hit will move to the table (to negotiate).''

The union would send pilots back to work for any company that agrees to negotiations, as long as the company does not do subcontracting work for big companies that refuse to talk.

''The problem is most of the small companies do sub for big companies,'' said Mr. Sasse.

The Coast Guard is taking a precaution as replacement pilots begin to look for relief.

''We're asking operators to push in (tie up the towboat and barges) at night if they have only one licensed pilot, and let us know where they are so we can keep track of them,'' said Lt. David Baugh, spokesman for the Coast Guard St. Louis Maritime Safety Office,

Craig Philip, president of Ingram Barge Co., said the 30-day mark will pass uneventfully. ''The strike hasn't been an issue,'' he said, asserting that only about 10 of Ingram's 225 pilots went on strike.

Owners say that insurance companies and the Coast Guard agree that accidents since the strike started may have happened anyway due to high waters.

Pilots Agree says the companies are dealing with safety issues by sticking their fingers in a crumbling dike.

''But rest assured the dike will burst, the flood is coming, and it will bring more danger to our nation's waterways,'' said Dickey Mathes, union president.

Lt. Baugh said he thought that, rather than endangering safety by using unlicensed pilots, owners would tie up towboats. ''Based on our experience, the operators have been real good about using pilots with proper licenses,'' he said.

One of the most serious incidents in the first month apparently was no accident.

On the night of April 24, one or more runaway barges slammed into barges tied up in a fleeting, or parking, area near the Jefferson Barracks Bridge in St. Louis. A chain reaction ensued that sent 137 barges careening in the current.

''The FBI is still investigating,'' said Lt. Baugh. ''They agree there's a good chance it was not an accidental release.''

Nearby tugs rounded up the breakaway barges in less than two hours with little damage caused. But the incident was fraught with danger.

One barge partially sank, but it was filled with grain, not with chemicals or other hazardous material.

Pilots Agree is helping the FBI determine what caused the breakaway, Mr. Sasse said.