One-way electric carsharing systems provide an environmentally friendly option for facilitating urban mobility needs. However, the management of one-way electric carsharing systems presents operational challenges stemming from the need to relocate cars in order to strike an optimum balance between demand and supply. As a result, the cost associated with vehicle relocation operations represents a significant proportion of the total operating cost. In the context of electric carsharing systems, the problem of vehicle relocation is further exacerbated by the car battery charging requirements. The introduction of temporal and spatial flexibility regarding the pick-up and drop-off of vehicles provides the means of improving the efficiency of one-way electric carsharing systems. However, the literature currently lacks models that can be used to investigate the effect of temporal and spatial flexibility on the performance of one-way electric carsharing systems. In this paper, we are introducing an integrated modeling and solution framework for investigating the effect of temporal and/or spatial flexibility, and different options for processing trip requests to the profitability and utilization of one-way electric carsharing systems. The application of the proposed framework to a realistic size system suggests that spatial flexibility has a stronger effect on the system performance than temporal flexibility. Furthermore, both spatial and temporal flexibility can increase the profitability of the system by serving more customers with fewer vehicle relocation needs.