Part showman but all business, Alan (Ace) Greenberg is the man who keeps the growl in the The Bear of Wall Street.

The 54-year-old chief executive of Bear Stearns & Co. is a magician, a bridge champion, and a big game hunter who has downed a wild cape buffalo and a wild boar in Africa with a bow and arrow. But his target at the moment is a unique company with a murky past and an uncertain future, whose assets at various times have been under the control of fallen financiers Bernard Cornfeld and John M. King and the fugitive Robert Vesco.

Called Global Natural Resources PLC, the company is based in the Channel Islands between Britain and France and controls sizable oil and gas reserves in remote places such as the jungles of Indonesia and the Canadian Arctic, as well as in the United States.

Fighting off The Bear's advances is Frank G. Beatty, the 61-year-old chairman of Global, who runs the world-wide concern from an office in a New Jersey suburb, across the Hudson River from Bear Stearns' crowded and hectic trading room in lower Manhattan.

The bruising fight for control of Global demonstrates the rough-and-tumble style of arbitragers like Bear Stearns, whose aggressiveness has earned it the title of The Bear.

At times the firm has as much as $5 billion of its own and its investors' capital at risk. Says Greenberg: "We'll take on anyone. We like to win, but win or lose, we'll take them on. After all, a doctor who only sets fingers never loses a patient."

The idea of making a play for Global was brought to the firm by two stockbrokers who had acquired large amounts of Global's stock. Ace Greenberg put together a group of wealthy and adventurous Bear Stearns clients, named the group the Committee for the Protection of Global Shareholders, then launched a two-prong financial and public relations attack.

Global was attractive because its assets have grown in value over the past 11 years with rising energy costs. Its oil and gas reserves, some of them located in remote regions, have become economical to exploit. Also, the company under Beatty invested $4 million in Indonesian oil and gas reserves, which by 1981 had increased in valued to $71 million. Even Beatty's enemies at Bear Stearns, who have little good to say about him, concede that this was a brilliant investment.

As a result, Global's earnings rose from $286,000 in 1974 (its first profitable year) to $18.1 million in 1981. The price of its stock, which is traded on the Frankfurt and London exchanges and over-the-counter in the United States, has been as high as $13 a share in recent weeks, up from 8 cents in 1971.

It's not clear what Bear Stearns will do with Global if it wins, but last year it proposed that the company be liquidated. The firm suggested that it be retained to sell off Global's assets and distribute the funds to the shareholders. Not surprisingly, Beatty rejected the plan.

With the showdown coming on Sept. 13 at the Global annual meeting on the Channel Island of Jersey, both sides are advertising in publications worldwide to seek the proxies of far-flung stockholders who live in some 170 countries (more than the membership of the United Nations).

What makes this proxy fight unique and complicated is that there is no record of who owns Global's 21 million shares. Global's common stock is in the form of bearer shares, which means that in order to vote, a stockholder must either go to the annual meeting or present his shares at a bank or brokerage and be certified to vote by proxy.

The reason for this unusual state of affairs can be traced to Global's tumultuous history. In the late 1960s, Cornfeld's vast Geneva-based financial conglomerate, Investors Overseas Services Ltd., was near collapse. Among its assets were oil and gas properties sold to it by John King and held by an IOS subsidiary, Global. At the time, King, a Denver oil and gas promoter, was among those bidding to take control of IOS.

In its struggle to remain liquid, IOS in 1970 spun off Global, whose holdings then had little cash value. IOS stockholders were encouraged to exchange their shares for stock in the new company. Since the laws of many nations didn't permit their residents to invest in IOS, bearer shares were issued to allow the investors to retain their anonymity.

By 1971, King's Denver firm, King Resources Co., which had invested heavily in teetering IOS, was bankrupt. Cornfeld, meanwhile, had been ousted from the insurance-mutual fund giant he had founded, and Robert Vesco, the obscure operator of a tiny electronics firm in New Jersey, had taken over. Vesco also put himself and his associates on the Global board of directors.

A year later, Vesco was also gone, allegedly absconding with more than $200 million of IOS' assets, according to a suit by the Securities and Exchange Commission. He has remained a fugitive from U.S. justice ever since.

Global and its affairs were taken over in 1972 by Beatty, who had been an officer and a director of Vesco's New Jersey company, International Systems and Controls, and who had been put on the IOS board by Vesco. (Beatty and other Vesco associates were sued by the SEC for their roles in the IOS takeover. Beatty settled with the agency without admitting or denying the allegations.)

Beatty insists that his ties to Vesco have long since been severed, that he in fact protected the assets of Global from Vesco, and that he hasn't seen him since 1973. Says Beatty: "Vesco at one point turned left, and I turned right."

But the Vesco connection continues to dog Beatty. It is a centerpiece in Bear Stearns' efforts to discredit him and gain control of Global. Beatty and management have responded in kind, attacking in advertisements the records of some members of the dissident slate.

The takeover battle had its beginnings in 1979 when two stockbrokers with A. G. Becker Inc. came across Global while researching investment opportunities in Canada for wealthy clients. The brokers, Stephen A. Springer and Anthony L. Geller, figured the company's oil and gas holdings were undervalued, making the stock a good investment.

The brokers also spotted the block of Global shares that remained unclaimed in the years since Global was spun off from IOS. Of Global's 21 million outstanding shares, about 1.2 million had never been claimed, and they were placed under a Canadian court because so many IOS investors had lived in Canada. The court assigned the shares to a trustee, who also was a Global director.

The two brokers began investing in Global for themselves, their families and customers, and were eager to establish a U.S. market for Global stock.

"We took Beatty to a number of mutual funds and institutional clients," says Springer, who suggests that he and his associate were doing a favor for Beatty by opening financial doors for him. "But we found Global totally unwilling to discuss in detail its properties, drilling plans, or goals."

Responds Beatty: "That's nonsense. They came to me twice, said they were trying to sell a block of Global. I went with them to meet the investment adviser. They were doing it to help themselves, not me."

In 1980, the two brokers left Becker and joined Bear Stearns. Soon after, The Bear went on the attack.

Springer says that he and his associate turned against Global because of manuevering by Beatty. On Dec. 22, 1980, Beatty's employment contract -- which still had one year to run -- was extended to his 68th birthday. The contracts for Beatty and Global's president were signed just four days before a new British law went into effect requiring shareholders' approval of directors' contracts.

The Bear Stearns group labels this self-dealing, but Beatty calls it self-protection. "We've been underpaid for years," says Beatty. "And with the company the subject of outrageous attacks and slander, the compensation committee gave us the contracts to keep us on the job."

Then, on June 21, Global agreed to buy another oil company -- just one day before another British law took effect requiring stockholder approval for such acquisitions. The Bear Stearns group argued that this again was a defensive maneuver and that the $44 million paid for the company was excessive, especially in light of the oil industry doldrums.

But what really enraged the dissidents was that Beatty paid for the McFarlane Oil Co. of Houston by issuing 3.25 million shares of stock from Global's inventory. The effect was to put newly issued stock into friendly hands, thereby diluting the strength of the Bear Stearns group's holdings. On Aug. 11, a London court denied a petition by the dissidents to block the McFarlane acquisition.

Last Wednesday the same court turned down an appeal of that decision. But the same day, a U.S. district judge in Cincinnati issued an order restraining the McFarlane acquisition until Sept. 3.

A Global spokesman called the Cincinnati decision "absolutely outrageous." He said that the company had asked the federal judge, S. R. Spiegel, to disqualify himself after he acknowledged being a friend of one of the dissidents, sports promoter and former ambassador to Switzerland Marvin L. Warner, who had filed the motion with the judge.

Noting that there is also a question about whether the U.S. court has jurisdiction over the British-based company, the spokesman said Global was "considering the course of conduct that's appropriate."

Global's management refuses to disclose how many proxies it holds, but the 3.25 million shares in the McFarlane deal could be critical to the outcome of the fight. Last April the Canadian trustee in charge of the 1.2 million unclaimed shares plunged to his death from a New York hotel room, and his replacement -- who is not a Global board member -- sold those shares to the Bear Stearns group.

The Bear Stearns forces now claim 4 million proxies. And recently Cornfeld announced that he controlled 830,000 shares of Global stock and would vote them with the dissidents.

But the Bear Stearns group, while it would be happy to get the proxies, wants to distance itself from Cornfeld, especially since it is trying to discredit Beatty by tying him to Vesco.

Says Ace Greenberg bluntly: "I don't want to be in the same room with him."