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We develop a dual payment New Monetarist model, where an electronic money (e‐purse) competes with fiat money (cash). The two payment instruments differ in terms of security, cost, and acceptability. Strategic complementarities lead to multiple monetary equilibria. We establish the conditions under which e‐money can coexist with, or replace fiat money, and explain the reasons for the e‐purse failure/success in a few countries. We also compare welfare when one currency or both circulate. When the risk of theft of cash is endogenous, e‐money cannot replace cash entirely; however, low inflation can facilitate the adoption of e‐money in parallel with fiat money. (JEL D83, E40, E50)