MEXICO CITY — When the authorities caught up with him at a lakeside hotel in Guatemala this past weekend, Javier Duarte, a fugitive former Mexican governor, went quietly.

Less than a week earlier, the Italian police had surrounded another former Mexican state governor, Tomás Yárrington, as he finished dinner at a restaurant on a Florentine piazza, ending his five years on the run.

At least three other former Mexican state governors are missing, and more than a half-dozen are under investigation or fighting prosecution on corruption charges. Whatever the accusations, the governors in this rogues gallery share at least one trait: All behaved as if they were untouchable.

“The decades of impunity have generated a level of audacity and absurdity that we have never seen in Mexico,” said Max Kaiser, an anticorruption expert at the Mexican Institute for Competitiveness, a research organization.