Firms that offer private tutoring and standardized-test preparation are scrambling to cash in on what could be a multibillion-dollar bonanza created by the No Child Left Behind Act (NCLB), which requires public schools to expose students to an unprecedented battery of assessments and offer tutoring, summer classes, and remedial instruction to those who fail.

Districts nationwide have turned to the private sector for help complying with the law, and in doing so have created a “supplementary educational services” industry that barely existed five years ago, executives said.

Princeton Review Chief Executive John Katzman said the company’s K-12 division, which runs after-school programs and helps students prepare for standardized tests, now has 2,000 client schools, up from none two years ago. The division now produces about 15 percent of the company’s business. Within three years, Katzman said he expects it to represent 25 percent.

National tutoring firms, such as Baltimore-based Sylvan Learning Systems, as well as companies that deliver supplemental curriculum online, such as Plato Learning and Pearson Education Technologies, also report a surge in demand from schools looking for outside help implementing extended-day programs.

“We serve about 70,000 kids today, and we feel like 70,000 kids is just scratching the surface,” said Sylvan executive Jeffrey Cohen. “We are talking about millions of kids in this country who have, over years and years, slipped far behind in their classes.”

Even New York City-based Edison Schools, best known as the nation’s largest for-profit manager of public schools, announced in late November that it is planning a rapid expansion of its fledgling summer-school and after-school program divisions. Within three years, it expects those operations to produce $100 million annually.

Supporters have hailed those developments, saying the private firms are riding to the rescue of schools that don’t have the personnel to tutor kids themselves.

But Monty Neill, executive director of FairTest, a group that has opposed the increased reliance on standardized testing, said the changes have happened too fast, with too little scrutiny of whether the new services actually help kids learn.

The Education Department’s final guidance for complying with NCLB specifies that states can require supplemental service firms to provide scientifically based research to support their offerings, much like schools are required to use only scientifically based products and methods to improve instruction in the core curriculum subjects. But states don’t have to hold supplemental service providers to this standard, according to the law.

“These private companies are really like vultures, descending on what they see as a feast,” Neill charged. “We’re worried that we are going to be hearing stories about schools not being able to buy library books because they are spending money on test prep.”

The law requires schools that don’t meet federal achievement standards to set aside between 5 percent and 20 percent of their federal antipoverty money for supplemental services.