By Claire Milhench

LONDON, April 28 (Reuters) - Libya's $67 billion sovereign wealth fund will go head-to-head with Societe Generale in London's High Court on Tuesday over claims the French investment bank paid $58.5 million in bribes to secure business from the fund.

The Libyan Investment Authority (LIA) is pursuing SocGen in relation to five trades totalling $2.1 billion, executed between 2007 and 2009, before Colonel Muammar Gaddafi was ousted as Libyan leader.

The LIA claims the trades were secured as part of a "fraudulent and corrupt scheme" involving the payment of $58.5 million by SocGen to a Panamanian-registered company called Lenaida, controlled at the time by Libyan businessman Walid Giahmi. Lenaida was dissolved in 2010.

In its latest annual report SocGen said that it "firmly refutes such allegations and any claim calling into question the lawfulness of these investments".

Giahmi, who is also named as a defendant in the suit, maintains that he is a legitimate businessman and there was never a fraudulent and corrupt scheme.

According to the LIA, Giahmi was in a position to act as a middleman because of his connections with what the fund calls 'Gaddafi Associates', in particular Saif Gaddafi, one of the leader's sons.

In a pre-trial hearing last May, the judge ruled in favour of the LIA's requests for further disclosure by Giahmi of phone and banking records to shed light on the nature of the alleged relationship.

Libya set up the LIA in 2006 with the aim of investing the large reserves accumulated from its oil revenues and integrating its economy into the international financial system after years of sanctions. It quickly became a magnet for foreign banks and fund managers.

The leadership of the LIA remains contested, in a dispute that mirrors the fragmented nature of the country since the fall of Gaddafi in 2011.

Last summer the fund lost a high-profile case against Goldman Sachs in which it tried to claw back $1.2 billion from the Wall Street firm in relation to nine equity derivatives investments carried out in 2008.

In that trial, the LIA argued that Goldman exercised "undue influence" and "unconscionable bargaining" to get it to enter the trades, and that it was too unsophisticated to understand what it was buying. However, the judge ruled in favour of Goldman, saying key decision-makers at the fund had understood the trades and the risks.

The LIA sought permission to appeal but is still waiting to hear the outcome of this.

The case against SocGen and Giahmi is more complex and involves allegations by the LIA that the payments to Lenaida were made with the aim of directly or indirectly influencing the LIA to enter into the disputed trades.

The trial is expected to run until July 31. Some witnesses appearing for SocGen will give evidence in private to avoid self-incrimination, as the French bank is also being investigated by U.S. authorities in connection with deals involving Libya.

In April 2014 the U.S. Department of Justice served Societe Generale with a subpoena requesting documents relating to transactions with Libyan entities and individuals, including the LIA.

In October 2016 the Securities and Exchange Commission served SocGen with a subpoena for the same purpose. Societe Generale said in its last annual report that it was cooperating with U.S. authorities.

(Reporting by Claire Milhench; Editing by Mark Trevelyan) ((claire.milhench@thomsonreuters.com; +44)(0)(207 542 3571; Reuters Messaging: claire.milhench.thomsonreuters.com@reuters.net))