SQUID Series Arrays (SSAs) are widely used amplification devices for cryogenic readout chains such as Transition Edge Sensor (TES) matrices for space observation (doi: 10.1007/s10686-022-09880-7) or quantum science (doi: 10.1063/5.0149478). Either wiring-related external or on-chip internal parasitics often cause SSAs to show instabilities, which may limit the obtainable gain from a SSA design or may constrain the cryogenic setup that can be made stable. We shall show a rough model of typical parasitics in a setup and estimate the associated stability criteria. Modelling is backed up with experimental data from SSAs fabricated at VTT ?(doi: 10.1109/TASC.2021.3060356) and operated at T = 4.2 K. In experiments the SSA has been augmented with a set of controlled external parasitic elements and the instability threshold observed.