By Paul P. Kennedy
Special to The New York Times

MEXICO CITY, July 7--Adolfo Lopez Mateos, candidate of the Administration's Instututional Revolutionary party, has been elected Mexico's next President.

Unofficial returns will not be announced for several dyas and the official returns will not be announced until Spetember.  But the Administration party clams that 90 percent of the total votes cast.  The principal opposition party, Natinal Action, is contending that the margin of victory of Senor Lopez Mateos will be smaller than first indicated, but there has been no argument over his triumph.

There also seems no doubt that yesterday's voting will prove to have been the heaviest in Mexico's history and also that it has been the most tranquil.  Thus far only one shooing incindent ha been reported.  It occurred in Ciudad Obregon in teh State of Sonora, where a man was killed as a result of what was called a local political quarrel.

The National Action party in a statement this morning charged that the election was "the most brutal jest ever perpetrated on the Mexican public."  The statement charged fradulent election practices and it was announced that an emergency meeting of teh party leaders would be called to discuss the charge.

An Administration party statement declared that the National Action party should dissolve itself as a result of its showing in the election.  It is the National Action party got more votes in yesterday's election than its 285,555 in the 1952 election, when the party ran a poor third.

The unofficial count, coming in at a slow pace, gave the following partial returns for the nineteen voting districts in the Federal District:  Senor Lopez Mateos, 329,480 votes against 94,225 for Luis H. Alvarez, candidate of the National Action party.

An Administration party spokesman said the Institutional Revolutionary party had elected its total slate of Deputies and Senators in the Federal District.

There are indication, however, that Fidel Velasquez, one of the Administrtion paty candidates for the Senate from the Federal District, had run into more serious opposition than expected.

Senor Velasquez, head of the Confederation of Mexican Labor and titular head of the so-called labor 'bloc," is the most important organized labor leader in Mexico.  He has been the subject recently of an attack by dissident labor groups.

One of the most powerful of these groups, the General Confederation of Workers, recently instructed its members to vote for the Administration party's Presidential candidate but not for the Congressional candidates of Senor Velasquez's organizatoin.