''If she has a document for entry and there is no reason to deny that entry, she can come in,'' said Berl Williams, acting agent in charge of the Immigration and Naturalization Service at Brownsville. ''The local crossing card is good for 72 hours. We don't stop pregnant women at the border.''

Although the children are citizens by virtue of being born on American soil, their parents are not. Thus, while new Americans like seven-month-old Abiel Leal have the same rights and entitlements as any other citizen, including free public education, Social Security, Medicare, voting, qualification to hold public office and so forth, his parents have little if any advantage.

''It does not aid the parents in gaining citizenship,'' said Mr. Williams. A Bus Trip to Brownsville

Nonetheless, Mrs. Leal thought that the opportunities were great enough on the day when she began to feel the contractions that signaled that the birth was near. She walked out of her house in Matamoros and caught a dusty local bus to the bridge leading to Brownsville and the United States. There she got out and walked across, showing the border guards her 72-hour visitor's pass.

At the end of the bridge, she walked the five blocks to the home of Mrs. Garcia, who had been recommended to her as ''the best.'' Mrs. Garcia's little house, crammed with knick-knacks, ceramic dolls and pictures of Jesus, is both home and birth clinic, with two tiny rooms with a cot in each for delivering babies.

On the front of the house, which is painted bright yellow and trimmed with blue, is a vivid blue sign decorated with a pair of storks bearing bundles and the words ''Se Atendien Partos,'' meaning ''Births attended here.'' 'I'm Not the Only One'

By the time Mrs. Leal reached the house at 7 A.M., the contractions had quickened, and four hours later, with Mrs. Garcia's help, she gave birth to Abiel.