By Luciana Magalhaes and Matthew Cowley 

SÃO PAULO--Two important shareholders of Brazil's largest medical-diagnostics company, Diagnosticos da America SA, or DASA, have secured a controlling stake in the firm in an auction Monday, the latest evidence of the demand for medical diagnostics companies.

Businessman Edson Bueno and his ex-wife, Dulce Bueno, bought 119.5 million shares of the firm in a deal valued at $747 million.

The move represents a new investment strategy for Mr. Bueno and his wife, who in 2012 sold a 90% stake in Brazilian health insurance firm Amil Participações SA to U.S.- based giant UnitedHealth Group for $4.3 billion.

The purchase had been opposed by some of DASA's shareholders, including OppenheimerFunds, which said the firm was undervalued. Oppenheimer rejected the tender offer in January, according to people familiar with the situation. The investment firm declined to comment for this article.

The Buenos had originally said the tender offer would only proceed if they secured sufficient shares to take control of DASA. However, in light of the shareholder opposition, they changed the terms, maintaining the offer price but withdrawing the condition for achieving the controlling stake.

Mr. Bueno declined to be interviewed for this article.

DASA is currently the largest firm in the Brazilian diagnostic industry with revenues of 1.8 billion Brazilian reais ($750 million) in the first nine months of 2013. The firm has an estimated 12% share of the Brazilian market, according to data provided by Fitch Ratings.

The other major player in Brazil, Fleury SA, could also change hands in the coming future. A handful of local and international private-equity funds, including Carlyle Group and Brazil's Gavea Investments, have engaged in negotiations in the local unit of J.P. Morgan, to possibly buy Fleury, according to people familiar with the talks. J.P. Morgan was hired to represent Fleury in those negotiations, the same people said.

J.P. Morgan, Fleury and the private-equity funds declined to comment for this article.

The Brazilian health care market has plenty of room to grow given the rising prosperity after some two decades of relative economic stability, according to analysts.

Despite a number of recent acquisitions by both DASA and Fleury, the market remains highly fragmented, and is divided among many small players. There are currently more than 5,000 health care service centers that serve private health plans in the country, Moody's Investors Service said in report in January.

"We believe that, in a fragmented industry, larger players like Fleury and DASA are in a more advantageous situation and have broader bargaining power when dealing with health insurance providers and hospitals," Moody's wrote in the report.

Write to Luciana Magalhaes at luciana.magalhaes@wsj.com and Matthew Cowley at matthew.cowley@wsj.com

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