This paper deals with the analysis of a multi-item, continuous review model of two-location inventory systems for repairable spare parts, used for expensive technical systems with high target availability levels. Lateral and emergency shipments occur in response to stockouts. A continuous review basestock policy is assumed for the inventory control of the spare parts. The objective is to minimize the total costs for inventory holding, lateral transshipments and emergency shipments subject to a target level for the average waiting time per demanded part at each of the two locations. A solution procedure based on Lagrangian relaxation is developed to obtain both a lower bound and an upper bound on the optimal total cost. The upper bound follows from a heuristic solution. An extensive numerical experiment shows an average gap of only 0.31% between the lower and upper bounds. The experiment also gives insights into the relative improvement achieved by applying lateral transshipments and or the system approach. We also apply the proposed model to actual data from an air carrier company.