Monoclinic alpha-Li3V2(PO4)(3) is a promising cathode material for future Li-ion batteries due to its high theoretical capacity, good capacity retention and relatively high ionic conductivity. The material undergoes a series of complex phase transitions which depend on the number of Li-ions extracted during charge. The phase behavior has been extensively studied under (quasi-) equilibrium conditions, however insight into the phase evolution during dynamic conditions is lacking. Through operando synchrotron X-ray diffraction we report the complex series of structural phase transitions under dynamic battery charge-discharge conditions in alpha-Li3V2(PO4)(3) cathodes with extraction of both two and three Li-ions. For extraction of two Li-ions, the phase evolution follows the series of expected two-phase transitions, while for extraction of three Li-ions the dynamic phase behavior differs significantly from that observed by equilibrium studies, e.g. we reveal unexpected solid solution behavior during removal of the last Li-ion and unforeseen structural hysteresis between charge and discharge. Our results are further reinforced by electrochemical analysis. This paper joins a series of recent reports, where extended solid solution behavior in battery electrode materials is observed under operando conditions, and reinforces the importance of these types of measurements to provide a more realistic picture of working battery materials.