In this paper we demonstrate that the extended linear expenditure system with durables (DELES) satisfies the first-order conditions for local unidentifiability, and discuss alternative methods that might be used to achieve identifiability, as well as their implications. Estimates are then presented of the linear expenditure system (LES), the extended linear expenditure system (ELES) and DELES, under each of two alternative error specifications, using seasonally adjusted, quarterly Australian data from 1959(4) to 1976(2). The two main purposes of this exercise are: (i) to compare the effects of allowing for first-order autocorrelation in LES and ELES; and (ii) to gauge the contribution of DELES to the linear expenditure family by making corresponding comparisons with ELES. When we fix the decay rate for durables a priori, in an attempt to secure identifiability, the estimates of the remaining parameters are insensitive to the value chosen. This suggests a major difficulty in interpreting DELES and leads us to reconsider its limiting properties.