We introduce modulation type spaces associated with the generators of polynomially bounded groups. Besides strongly continuous groups we study in detail the case of bi-continuous groups, e.g. weak-continuous groups in dual spaces. It turns out that this gives new insight in situations where generators are not densely defined. Classical modulation spaces are covered as a special case but the abstract formulation gives more exibility. We illustrate this with an application to a nonlinear Schrödinger equation. Mathematics Subject Classification (2010). 47D06, 47A60, 47D08, 35Q55.