A series of alkaline earth sulphate phosphors MSO4:Eu2+ (M =Mg, Ca, Sr, Ba) is obtained in doping experiments. It is discovered that these phosphors doped with Eu2+ ions have the thermoluminescence (TL) characteristics which are quite different from those in the alkaline earth sulphate phosphors doped with trivalent rare earth ions RE3+ (RE= Dy, Tm, Eu). It is also observed that there is only one glow peak in the three-dimensional emission spectrum and the radiation dose response of the glow peak is linear-sublinear in the series of phosphors MSO4:Eu2+ (M =Mg, Ca, Sr, Ba). However, quite a lot of experimental results show that there are several glow peaks in the three-dimensional emission spectrum, and the TL radiation dose responses are linear-supralinear in the series of phosphors MSO4:RE3+ (M =Mg, Ca, Sr, Ba and RE= Dy, Tm, Eu). The reason lies in the structures of defect complexes which are formed in the course of preparation of these phosphors and include intrinsic imperfects and dopants. These defect complexes can be regarded as basic elements in the TL multi-stage process. In the series of phosphors MSO4:Eu2+ (M =Mg, Ca, Sr, Ba), the isoelectronic traps produced by doping Eu2+ ions which have the same valences as superseded alkaline earth ions are very localized traps to form the defect complexes (Eu2+ isoelectronic trap-SO42-) that are basic elements in the TL multi-stage process, in which there are one-hit TL events basically. However, in the MSO4:RE3+ (M =Mg, Ca, Sr, Ba) phosphors, the defect complexes (RE3+-SO42--cation vacancy VM) are basic elements in the TL multi-stage process, in which there are two-hit TL events basically. It is clear that the Eu2+ isoelectronic trap phosphors play key roles in TL Characteristics in MSO4:Eu2+ (M = Mg, Ca, Sr, Ba). In addition, it has been observed that the wave length at the single TL peak in each of the three-dimensional emission spectra of the series of phosphors MSO4:Eu2+ (M =Mg, Ca, Sr, Ba) is related to the substrate of each of these phosphors, such as the wave lengths at the TL peaks are 440, 385, 375 and 375 nm for MgSO4:Eu2+, CaSO4:Eu2+, SrSO4:Eu2+, and BaSO4:Eu2+ respectively. The experimental results display the characteristics of Eu2+ isoelectronic traps formed by substituting alkaline earth ions which have different cationic radii and electronegativities. The SrSO4:Eu2+ phosphor can be called typical isoelectronic trap phosphor which has the higher TL and optical stimulated luminescence efficiency.