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The UPACK program for crystal structure prediction was extended to allow the possibility of more than one molecule in the asymmetric unit. A search method was developed where the essential parameters (including torsional angles of hydroxyl groups) take random values. Energy minimization and clustering then lead to a list of hypothetical structures. In a test for six hexapyranoses this random search method was found to be approximately equally as efficient as the previously used systematic grid search method for one independent molecule. As a second test, the generation of structures with more than one independent molecule was performed for ethanol. A multitude of possible structures was found, the experimental one (two independent molecules in space group ) always being present. However, for -D-mannose (two independent molecules with five unknown hydroxyl torsional parameters each) the number of hypothetical structures was so large that the experimental structure was never encountered. Finally, a crystal structure generation for hydrates of pyranoses and polyalcohols was carried out. When the total number of unknown parameters was less than 20, the experimental structure was encountered. As usual, the empirical energies were not adequate to select that structure from the list of possible ones. Even then, the procedure proved to be valuable in identifying the most probable hydrogen-bonded network in cases where hydrogen positions in the experimental crystal structure were missing.