The strongly pronounced obstructive sleep apnoea syndrome can lead to serious traffic accidents if the driver falls asleep at the wheel. This article deals with the insurance law consequences, especially with the problem if the insurer raises the objection that the sleep apnoea sufferer acted grossly negligent. Since the new German Insurance Contract Act of 1 (st) January 2008 paragraph 81 regulates a benefit reduction in cases of gross negligence by the insurant. The insurer can shorten assurance benefit according to the degree of fault. In the literature it is proposed to grade the level of grossly negligence into low, middle and serious forms of default. Usually the driver notices clear signs of exhaustion in the current state of medical science. If he ignores obvious facts of exhaustion the insurer can shorten assurance benefits percentual. When the driver dozes off after a long trip although he has noticed his exhaustion, a case of gross negligence exists. Here the insurer can reduce the assurance benefit by about 50 %. Does the sleep apnoea sufferer always act in a grossly negligent manner in cases of microsleep? This point has not yet been decided by the German jurisdiction in favour of the policyholder. The jurisdiction is aware of the fact that in the case of sleep apnoea fatigue does not necessarily need to precede the act of falling asleep. In the opinion of the author it has to be distinguished between medicated and not medicated sleep apnoea and further if the sufferer knows about his disease. If the sleep apnoea sufferer has known of the risk of sudden microsleep, for example, after being warned by his doctor who discovered the disease, gross negligence cannot be dismissed and assurance benefit has to be reduced by about 65 %.