Recently it has been shown by exclusive and kinematically complete experiments that the appearance of a narrow resonance structure in double-pionic fusion reactions is strictly correlated with the appearance of the so-called ABC effect, which denotes a pronounced low-mass enhancement in the ππ-invariant mass spectrum. Whereas the resonance structure got its explanation by the d∗(2380)dibaryonic resonance, asat-isfactory explanation for the ABC effect is still pending. In this paper we discuss possible explanations of the ABC effect and their consequences for the internal structure of the d∗dibaryon. To this end we examine and review a variety of proposed explanations for the ABC effect, add a new hypothesis and confront all of them with the experimental results for the np→dπ0π0and np→npπ0π0reactions, which are the most challenging ones for this topic.
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