Primary complex Hopf surfaces are quotients of C^2 \(0,0) by a group G generated by a contracting automorphism of C^2 fixing the origin. These are non-algebraic surfaces homeomorphic to S^1 x S^3. The classification of these surfaces is reduced to the classification of contracting germs and follows from the Poincare-Dulac theorem for normal forms. The same classification of normal forms for contracting germs works over non-Archimedean fields and gives the classification of non-Archimedean Hopf surfaces (Voskuil). Over the tropical semi-field the action and classification of germs is delicate due to the idempotency of addition. We use modifications to “monomialize” contracting tropical germs and construct tropical analogues of Hopf surfaces. This is joint work with Matteo Ruggiero.