The objective of this paper is to analyse the influence of a non-ideal grid over hysteresis controllers of converters connected to the grid through both L and LCL filters. The paper will describe the different possible configurations in both cases, analysing the effect of a general R-L grid. Limit values for both grid inductance and resistance are given for the L structure. In the case of LCL connection, the analysis will overview important issues such as active damping, and switching behaviour giving limits to stability as a function of grid impedance value.