More than 10 months after the deal was first announced, Clear Channel Communications Inc. shareholders will get the chance to vote on a proposed $19.5 billion buyout of the radio giant.

The offer from a private equity group led by Thomas H. Lee Partners LP and Bain Capital Partners LLC was first announced in November but was sweetened several times after some large shareholders signaled they would oppose earlier offers.

The shareholders meeting is scheduled for Tuesday in San Antonio, where Clear Channel is based.

The latest offer of $39.20 per share in cash or stock has appeased at least some of the big holdouts against what could become a privately owned company. Current shareholders could end up with as much as 30 percent of the new company.

“It now appears that all parties are prepared to move forward,” said Stanford Group analyst Frederick Moran. “We’ve undoubtedly seen advertising demand for historical media like radio slow down during the summer and into the third quarter. ... The $39.20 offer looks even better.”

Those who choose to keep shares in the new company will be issued shares that are expected to trade over-the-counter and will not be listed on any major exchange, according to company filings last month with the Securities and Exchange Commission.

The buyers will assume $8 billion in debt.

Two-thirds of shareholders must approve the buyout, and previous offers of $37.60 and $39 per share were deemed too low by some and weren’t expected to pass. Analysts have said the latest offer will likely be enough to win over the holdouts.

“It appears that all the stars have aligned,” Moran said. “We also think that the credit crunch and the shaky stock market environment over the summer causes more comfort on behalf of shareholders to approve the deal.”

The offer to allow shareholders to keep part of the newly private company is an unusual concession because private equity buyers pay a premium to get total control and fewer regulatory requirements than those required of public companies.

If approved by shareholders, the deal is expected to close before the end of the year.

Shares of Clear Channel fell 12 cents to $36.76 Monday.