Hedge funds are among the most mysterious institutions operating in the financial markets. Their influence upon the market is ambiguous - on one hand, they improve liquidity, but on the other the excess absorption of risk, including credit risk, may lead to materialization of the W. Buffet's thesis, that credit derivatives in hedge fund portfolios may became a weapon of mass destruction A complexity and uniqueness of the strategies they apply requires discretion and lack of conservative framework of regulations, which can be accepted, if we assume, that their offer is addressed to the "top" segment of the private banking sector, with additional security measures in the form of the necessity to verify the material status of investors, and a ban on advertising of participation units. The problem begins, when banks or pension funds became investors, since they cannot legitimately invest in risky speculative ventures, or limit credit risk by transactions with hedge funds (which often makes such hedging illusory). A significant influence of hedge funds upon the financial market was noticed by the international regulatory bodies co-operating within the Basel Committee on Banking Supervision. The Financial Stability Forum was established in 1999. Its works resulted in the following conclusions regarding the key factors increasing the risk of destabilization of the financial markets - insufficient banking supervision in tax havens, - inappropriate monitoring of risk connected with operation of hedge funds. For the time being, the correct conclusions formulated by the Forum of Financial Stability were not reflected in the appropriate supervisory regulations. In the context of growing influence of hedge funds upon the financial market and its stability, the following risk-limiting solutions are worth considering: 1) a necessity to treat hedge funds similarly, as other participants of the market of non-stock-exchange derivative instruments (the ISDA standard and security deposits beyond the threshold value) 2) introducing the category of "acceptable contractor" in futures transactions, which would limit the growing share of hedge funds in the structure of sellers of hedging, and allow for separate treatment (in the regulatory sense) of exposures with "acceptable contractors", and of those with other parties (a similar solution is recommended in the New Capital Accord), 3) obliging every hedge fund to obtain external rating, which would not signify a disclosure of the funds' investment policies, but would provide investors with an objective evaluation of funds. The proposed attitude would limit investments in low rated hedge funds by banks and investment and pension funds. The diversity of hedge funds may prove a problem in this respect, also in terms of appetite for risk, so perhaps the primary action should be classification of funds before granting them ratings within their particular category (author's abstract)