This paper examines with the help of a theoretical setting the properties of two blockchains' consensus protocols (Proof of Work and Proof of Stake) in the management of a local (or networks of local) complementary currency(ies). The model includes the control by the issuer of advantages of the use of the currency by heterogeneous consumers, and the determination of rewards of also heterogeneous validators (or miners). It considers also the resilience of the validation protocols to malicious attacks conducted by an individual or pools of validators. Results exhibit the interest of the Proof of Stake protocol for small communities of users of the complementary currency, despite the Proof of Work Bitcoin like system could have advantages
when the size of the community increases.