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This paper studies the monotonicity of equilibrium costs and equilibriumloads in nonatomic congestion games, in response to variations of the demands.The main goal is to identify conditions under which a paradoxical non-monotonebehavior can be excluded. In contrast to routing games with a single commodity,where the network topology is the sole determinant factor for monotonicity, forgeneral congestion games with multiple commodities the structure of thestrategy sets plays a crucial role.  We frame our study in the general setting of congestion games, with a specialfocus on singleton congestion games, for which we establish the monotonicity ofequilibrium loads with respect to every demand. We then provide conditions forcomonotonicity of the equilibrium loads, i.e., we investigate when they jointlyincrease or decrease after variations of the demands. We finally extend ourstudy from singleton congestion games to the larger class of constrainedseries-parallel congestion games, whose structure is reminiscent of the conceptof a series-parallel network.

Monotonicity of Equilibria in Nonatomic Congestion Games