Many plant species of agriculture importance are polyploid, having more than two copies of each chromosome per cell. In this paper, we describe statistical methods for genetic map construction in autopolyploid species with particular reference to the use of molecular markers. The first step is to determine the dosage of each DNA fragment (electrophoretic band) from its segregation ratio. Fragments present in a single dose can be used to construct framework maps for individual chromosomes. Fragments present in multiple doses can often be used to link the single chromosome maps into homologous groups and provide additional ordering information. Marker phenotype probabilities were calculated for pairs of markers arranged in different configurations among the homologous chromosomes. These probabilities were used to compute a maximum likelihood estimator of the recombination fraction between pairs of markers. A likelihood ratio test for linkage of multidose markers was derived. The information provided by each configuration and power and sample size considerations are also discussed. A set of 294 RFLP markers scored on 90 plants of the species Saccharum spontaneum L. was used to illustrate the construction of an autopolyploid map. Previous studies conducted on the same data revealed that this species of sugar cane is an autooctaploid with 64 chromosomes arranged into eight homologous groups. The methodology described permitted consolidation of 54 linkage groups into ten homologous groups.