The spontaneous spreading of thin liquid films over substrate surfaces is attracting much attention due to its broad applications. Under particular conditions, surfactants deposited on substrates exhibit unstable spreading. In spite of the large effects of the stability of the spreading on the accuracy and efficiency of industrial processes that use the spreading, understanding how the stability of the spreading process is governed by the physical and chemical properties of the system is still little known. Recently, ionic liquids have been characterized as a new kind of surfactant due to their special properties. Here, we investigate the stability of the spreading of deposited imidazolium-based ionic liquids on an aqueous substrate. We focus mainly on the effects that the water solubility of the ionic liquids has on the stability. Hydrophobic ionic liquids exhibit spreading that has a highly periodic and petal-like unstable spreading front, whereas hydrophilic ionic liquids spread without such a regular spreading front and their spreading area shrinks after reaching its maximum. We propose a model for the generation of unstable spreading of hydrophobic ionic liquids, i.e., the unstable spreading front is created by the penetration of oncoming water in front of the spreading tip into the more viscous spreading ionic liquid layer, like the viscous fingering that occurs in a Hele-Shaw cell. However, the direction of the penetration is the opposite of the direction that the interface moves (the spreading direction), which is contrary to that in viscous fingering.