This paper proposes two metaheuristics based on large neighbourhood search for the PEVRP (Periodic Electric Vehicle Routing Problem). In the PEVRP a set of customers have to be visited, one times, on a given planning horizon. A list of possible visiting dates is associated with each customer and a fixed fleet of vehicles is available every day of the planning horizon. Solving the problem requires assigning a visiting date to each customer and defining the routes of the vehicles in each day of the planning horizon, such that the EVs could be charged during their trips at the depot and in the available external charging stations. The objective of the PEVRP is to minimize the total cost of routing and charging over the time horizon. The first proposed metaheuristic is a Large Neighbourhood Search, whose choice of destroy/repair operators has been determined according to the experimental results obtained in previous research. The second method is an Adaptive Large Neighborhood Search, which could be described as a Large Neighborhood Search algorithm with an adaptive layer, where a set of three destroy operators and three repair operators compete to modify the current solution in each iteration of the algorithm. The results show that LNS is very competitive compared to ALNS for which the adaptive aspect has not made it more competitive than the LNS.