A simple but sensitive horizon test is described to determine whether the mesophases of molten organic salts exhibit any detectable elastic-plastic threshold, before they begin to flow under even very small applied shear stresses. By using this test with sodium isovalerate (mesophase range 188-280 degrees C) no detectable threshold is found above about 260 degrees C; above this temperature the melt thus behaves as completely fluid. However, between this temperature and the first melting point (188 degrees C) a definite limit stress appears to be required to start flow. Other properties of the mesophase also show changes around 260 degrees C with some analogies to fluid-glass transitions in other systems. Molten sodium n-butyrate, when tested in a similar way, fails to exhibit any distinctive elastic-plastic threshold. So far as can be detected by the horizon test, it remains completely fluid over the whole of its mesophase range (252-324 degrees C).