Citicorp and Manufacturers Hanover Corp. yesterday reported 1982 earnings gains despite increases in loan-loss provisions.

Citicorp, holding company for Citibank, the nation's second largest, said 1982 earnings before securities transactions rose 35 percent to a record $747 million ($5.78 a share) from $555 million ($4.40) in 1981. Securities losses reduced net income to $723 million ($5.60), up from $531 million ($4.20) in 1981.

Citicorp said a 26 percent rise in total revenue in 1982 to $5.2 billion "significantly outpaced" the 16 percent increase in operating expenses.

Citicorp's nonperforming loans--those on which little or no interest is received--totaled $1.7 billion, an increase of $626 million from 1981, with "Mexican and other Latin American private-sector borrowers representing the largest component of the increase."

Provision for loan losses was increased to $473 million from $305 million in 1981, Citicorp said. Net chargeoffs were $376 million, up from $256 million the previous year.

Manufacturers Hanover Corp., whose subsidiary Manufacturers Hanover Trust is the fourth-largest U.S. commercial bank, said 1982 earnings before securities transactions were $296.3 million ($7.82 a share), up from $256.5 million ($7.61) in 1981.