A discrete-time dynamic hedging problem is solved under expected utility maximization and basis risk without imposing a particular parametric form for utility, nor assuming normally distributed cash and futures prices. The solution is valid for any increasing and strictly concave utility function, and for quite general specifications of the joint distribution of cash and futures prices. This generality is achieved by restricting the futures market to be unbiased, and requiring that the size of the cash position be nonstochastic. The dynamic hedging rule can be estimated empirically using similar methods to those used to estimate static hedge ratios. Copyright 1996, Oxford University Press.