An economically viable method of fermenting a mixture of sugars resulting from the acid hydrolysis of material containing cellulose and hemicellulose allows for the simultaneous fermentation of both pentose and hexose sugars. The sugar solution is mixed with a microbial organism known to produce a useful fermentation product, and the fermentation process is allowed to proceed for 3-5 days, during and after which the fermentation products are removed and purified.