This paper presents a methodology to perform online self-testing for analog circuits implemented on field-programmable analog arrays (FPAAs). It proposes to partition the FPAA circuit under test into subcircuits. Each subcircuit is tested by replicating the subcircuit with programmable resources on the FPAA chip, and comparing the outputs of the subcircuit and its replication. To effectively implement the proposed methodology, this paper proposes a simple circuit partition method and develops techniques to address circuit stability problems that are often encountered in the proposed testing method. Furthermore, error sources in the proposed testing circuit are studied and methods to improve the accuracy of testing results are presented. Finally, experimental results are presented to demonstrate the validity of the proposed methodology.