Barcelona — Psychologist Angels Corcoles recently taught a seminar about self-empowerment for women, and when she finished she got a check with her fee. The amount was in hours, not euros.

But Corcoles didn’t mind. Through a citywide credit network that allows people to trade services without money, the 10 hours Corcoles earned could be used to pay for a haircut, yoga classes or even carpentry work.

At a time when the future of the euro is in doubt and millions are unemployed or underemployed with little cash to spare, a parallel economy is springing up in parts of Spain, allowing people to live outside the single currency.

In the city of Malaga…