This paper aims to develop a framework for logistics service capability of logistics service provider (LSP), to structure a model on analytic hierarchy process – method and to apply this model in the contexts of third party logistics and fourth party logistics service providers. Based on the literature review we formed a framework about the individual capabilities and components contributing to logistics service capability of LSP company. We approved AHP for exploring which of those logistics service production related capabilities are significant for operational performance of LSP and, are there differences between 3PL and 4PL performance. This case study addressed that in relation to identified logistics service capabilities the performance was quite equal, but 3PL was slightly better in demand and process capability groups whereas 4PL rose a little above 3PL in information and coordination capability groups.