Genetic mismatch scanning has been suggested as a method for using affected pairs of ostensibly unrelated but putatively distantly related affecteds in isolated populations to map disease genes. We model the regions of identity-by-descent of these affected pairs as a continuous time two state process with unknown parameters that depend on the (unknown) relationships, and we estimate the unknown parameters from the observed data. Simulated data involving pairs of first to fourth cousins show that the procedure thus obtained has properties similar, albeit slightly inferior, to the case where the relationships of the affected pairs, hence the parameters governing the processes, are known.