MPLS-based path technology shows promise as a means of realizing reliable IP networks. Real-time services such as VoIP and video-conference supplied through a multi-domain MPLS network must be able to guarantee end-to-end QoS of the inter-domain paths. Thus, it is important to allocate an appropriate QoS class to the inter-domain paths in each domain traversed by the inter-domain paths. Because each domain has its own policy for QoS class allocation, it is necessary to adaptively allocate the optimum QoS class based on estimation of the QoS class allocation policies in other domains. This paper proposes two kinds of adaptive QoS class allocation schemes, assuming that the arriving inter-domain path requests include the number of downstream domains traversed by the inter-domain paths and the remaining QoS value toward the destination nodes. First, a measurement-based scheme, based on measurement of the loss rates of inter-domain paths in the downstream domains, is proposed. This scheme estimates the QoS class allocation policies in the downstream domains, using the measured loss rates of path requests. Second, a state-dependent type scheme, based on measurement of the arrival rates of path requests in addition to the loss rates of paths in the downstream domains, is also proposed. This scheme allows an appropriate QoS class to be allocated according to the domain state. This paper proposes an application of the Markov decision theory to the modeling of state-dependent type scheme. The performances of the proposed schemes are evaluated and compared with those of the other less complicated non-adaptive schemes using a computer simulation. The results of the comparison reveal that the proposed schemes can adaptively increase the number of inter-domain paths accommodated in the considered domain, even when the QoS class allocation policies change in the other domains and the arrival pattern of path requests varies in the considered domain.