We design an adaptive observer for a stable single-input and single-output continuous descriptor (generalized state-space or singular) system. Under the assumption that the descriptor system is observable, it is transformed into what we call descriptor observer canonical form. This form also allows the descriptor variable to be represented by a linear combination of the 2n unknown parameters and the filtered input and output measurement. We also show that the estimates converge to the true values, when the bounded input satisfies the richness condition, under the assumption that the system is controllable.