We consider nonlinear Schrödinger equations in Fourier-Lebesgue and modulation spaces involving negative regularity. The equations are posed on the whole space, and involve a smooth power nonlinearity. We prove two types of norm inflation (strong ill-posedness) results. We first establish norm inflation results below the expected critical regularities. We then prove norm inflation with infinite loss of regularity under less general assumptions. We shall also discuss similar results for fractional Hartree equation. The talk is based on a joint work with Remi Carles and Saikatul Haque.