Rogelio Zambrano Lozano, 57, board member since 1987 and a cousin of the late CEO, will take over as chairman of the board, Cemex added in a statement, as the company separates the dual roles that Lorenzo Zambrano held.

Questions have swirled this week after Zambrano, who had been Cemex CEO for three decades, died of natural causes at age 70 in Madrid on Monday, leaving no public succession plan.

Zambrano built Cemex, one of Mexico's biggest listed companies, into a modern multinational with a presence on five continents.

But the company has struggled with large debts and cost-cutting since Zambrano's ill-timed $16 billion takeover of Australian rival Rinker in 2007, when the U.S. housing market was already months into a downturn.

Gonzalez, 59, joined the company in 1989, and was closely involved in and damaged by the Rinker acquisition.

But Gonzalez, who has worked all over the world, is seen by analysts as a key figure in Cemex's debt refinancing and its slow path to health.

"Cemex's strategy has been maintained for many years and it will continue to be maintained," said Gonzalez on Wednesday after attending a mass honoring the late CEO, referring to the cement maker's international presence.

Cemex was founded by Lorenzo Zambrano's grandfather, but it was Lorenzo who turned it into an international company with a broad investor base through a series of acquisitions. He had a small stake in the company that went public in Mexico in 1976 and listed on the New York Stock Exchange in 1999.

In 2006, Zambrano was among Mexico's wealthiest people, worth an estimated $1.8 billion. But his fortune tumbled after the Rinker purchase and he fell off Forbes' richest list.

The company's share price has fallen nearly 3 percent since Zambrano's death.

Lorenzo Zambrano's nephew Ian Armstrong Zambrano was also named as a new board member, subject to shareholder approval, the company statement said.

(Reporting by Christine Murray and Gabriela Lopez; Writing by Alexandra Alper; Editing by Simon Gardner and Ken Wills)