Traditional empirical analysis of consumer demand has usually made the assumption of linear budget sets. That is, the consumer is assumed to purchase any desired quantity at a constant price subject to a budget constraint. However, empirical situations with nonconstant prices occur because of taxes, two part tariffs, and more generally when the cost of utilization of a durable good varies with its purchase price. This paper discusses econometric approaches to consumer demand with nonlinear budget sets. An empirical example with choice under uncertainty in the presence of nonlinear budget sets is also presented.