Are local complementary currencies doomed? We analyse the conditions underlying the existence of these alternative monetary arrangements from the perspective of the two-sided platform theory. Considering their benefits to depend on the cross-externality generated by the presence of buyers and sellers using the alternative means of payment, we show that the possibility of the sustainability of such arrangements is weak. The result is established in a very general setting and with few restrictions on the parameters. Except in the presence of subsidies, the odds are low for local complementary currencies to survive.