This paper describes a new built-in self test (BIST) technique suitable for both functional and structural testing of analog and mixed-signal circuits based on the oscillation-test methodology. Analog-to-digital converter (ADC) is used as a test vehicle to demonstrate the capability of the proposed OBIST technique for both functional and structural testing. Design of different parts of OBIST structure is also presented. The ADC conversion rate, differential nonlinearity (DNL) and integral nonlinearity (INL) at each quantization band edge (QBE) are tested as functional parameters. These parameters are considered to be the most important functional characteristics of an ADC. Practical experimentation using real-world successive approximation and flash ADCs confirms the accuracy of OBIST for functional testing of ADCs. Simulation results using a 3-bit flash ADC designed using a CMOS 1.2 mu m technology are also presented. For structural testing, oversampled sigma-delta ADCs are investigated. Both hard and soft faults are considered and some simulation results are presented.