Shortest path problem in a network is a fundamental task in combinatorial optimization. Many applications in practice involve optimization two conflicting criteria and from a biobjective shortest path problems. Since there does not exist a single solution that is optimal with respect to both objective functions, we are interested in a special set of solutions for which any of the two criteria cannot be improved without declining the other: Pareto optimal set or Pareto front. In this paper we analyze in details the biobjective shortest path problem in the case in which the first objective function is a linear one (minimal length paths) and the second one is a nonlinear bottleneck function (maximal capacity paths). We present an exact solution based on two modifications of the Dijkstra’s algorithm that finds the complete description of all Pareto optimal solutions. We provide detailed poofs of the correctness and the computational complexity of the presented algorithms and numerical examples that illustrate their execution.