When dominant mutations of different genes may lead to the same disease, it is often difficult to detect in a particular patient which gene is involved. A strategy is to make genealogical extensions to find affected relatives that should have inherited the same mutation. In particular, for diseases with late age of onset or short survival time, only poor information may be obtained from close relatives of probands and it can be particularly efficient to make genealogical extensions to detect pairs of distantly related affected individuals. Such a pair of affecteds may provide information concerning the region of the genome where the mutated gene should map. Two situations may be encountered depending on whether or not prior information on the location of mutated genes involved in the disease are available. If we already know, from previous linkage studies, that a gene located in a given region R of the genome may be involved in the disease, the problem is then to confirm that it is indeed a mutation of this gene that is involved in the affected pair. Once the implication of a gene in region R has been confirmed the affected pair of relatives may give information to restrict the length of this region R. In this paper we discuss these two points by deriving analytically first the lod score expected and second the expected reduction of the length of the region where the mutation is suspected to map as a function of the number of meioses between the two affected individuals and of the polymorphism of the markers available in the region.