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This paper presents a discussion of the concept of threshold for trapped space charge accumulation in solid dielectrics submitted to a DC field. The starting point is the fact that it is often possible to define a critical field separating an ohmic type of conduction from a nonlinear regime in the current-voltage characteristic of solid dielectrics. In the space charge limited conduction theory, this critical field corresponds to the onset of space charge accumulation. However, other conduction processes, such as hopping conduction for example, can also explain nonlinearity in the current-voltage characteristic, which does not involve space charge. It is proposed to check for the existence of a critical field for space charge accumulation using complementary techniques, i.e., space charge detection and electroluminescence techniques. Polyethylene, polyester and polycarbonate were investigated as being representative of three different families of polymers. It is shown that similar values of thresholds are found for a given material using the three above-mentioned techniques, lending support to the physical explanation of a threshold for trapped space charge accumulation.