The resource allocation problem is a fundamental problem in Grid and Cloud computing environments. This paper focuses on constructing nondominated (ND) local coteries to solve the problem in a distributed way. Distributed algorithms using coteries usually incur low communication overhead and have high degree of fault-tolerance, and ND coteries are candidates for the algorithms to achieve the highest degree of fault-tolerance. A new type of coteries, called p-coteries, is defined to aid the construction of local coteries. Theorems about the nondomination of p-coteries are then developed, and an operation, called pairwise-union (p-union), is proposed to help generate ND p-coteries, which in turn can be used to generate ND local coteries for solving the resource allocation problem.