Summary: The use of personal identity verification systems with multi-modal biometrics has been proposed in order to increase the performance and robustness against environmental variations and fraudulent attacks. Usually multi-modal fusion of biometrics is performed in parallel at the score-level by combining the individual matching scores. This parallel strategy exhibits some drawbacks: (i) all available biometrics are necessary to perform fusion, thus the verification time depends on the slowest system; (ii) some users could be easily recognizable using a certain biometric instead of another one and (iii) the system invasiveness increases. A system characterized by the serial combination of multiple biometrics can be a good trade-off between verification time, performance and acceptability. However, these systems have been poorly investigated, and no support for designing the processing chain has been given so far. In this paper, we propose a novel serial scheme and a simple mathematical model able to predict the performance of two serially combined matchers as function of the selected processing chain. Our model helps the designer in finding the processing chain allowing a trade-off, in particular, between performance and matching time. Experiments carried out on well-known benchmark data sets made up of face and fingerprint images support the usefulness of the proposed methodology and compare it with standard parallel fusion.