Two men control Mexico’s telecommunications and broadcast markets: Carlos Slim, one of the world’s richest men, and Emilio Azcarraga Jean, the son of a late Mexican media tycoon.

But a new bill expected to be presented Monday to a divided Congress in Mexico City is ostensibly aimed at loosening the pair’s grip on their respective industries, namely Slim’s America Movil SAB de CV (NYSE:AMX), which controls 70 percent of the mobile market and 60 percent of fixed lines in the country, and Azcarraga’s Grupo Televisa SAB (NYSE:TV), a longtime broadcast leader that holds 60 percent of the market, according to Reuters.

For years there has been debate over Slim’s control of telecommunications. In 1990 he acquired state-owned Telmex from the government. The deal attracted scrutiny because it was paid for in installments from the company’s revenue and underscored the cushy relationship between Mexican business and political elites. For years, the cost of phone services remained among the highest in the world.

For its part, Grupo Televisa has long been viewed as a mouthpiece for the Institutional Revolutionary Party (PRI), which lost control of Los Pinos (Mexico’s presidential palace) in a historic 2000 election but regained control last year with a victory by former state Gov. Enrique Peña Nieto. As in elections past, Televisa was accused by opposition parties of favoring the PRI candidate.

The president is expected to unveil the bill on Monday, which could result in a breakup of these two companies to help competition. But no party holds a definitive majority. For example, there are seven main parties in the Chamber of Deputies – Mexico’s lower house of Congress – and none can pass legislation without wooing members of other parties. The PRI holds the largest chunk of the Chamber, but the conservative National Action Party (PAN) holds a majority in the Senate.

Opposition groups have said they fear any bill that would come out of a PRI-PAN negotiated process – necessary for the bill to pass both houses – would not go far enough to break Slim’s and Azcarraga’s control over a large share of the country’s telecommunications and broadcasting markets. If past efforts at breaking the bond between private enterprise and the state are any indication, they have reason to be concerned.