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We study limits of (∞, 1)-categories with structure and the lax morphisms between them by introducing the notion of enhanced simplicial categories. We establish that many interesting enhanced simplicial categories, including that of (∞, 1)-categories with limits, and that of (discrete) Cartesian fibrations between (∞, 1)-categories, admit several kinds of limits that involve lax morphisms in the diagrams, such as Eilenberg-Moore objects over monads that are lax morphisms, and ∞-categorical versions of inserters and equifiers of lax morphisms. We also establish the dual versions for (∞, 1)-categories with colimits, and (discrete) coCartesian fibrations, and analogous results for two-sided fibrations between (∞, 1)-categories. Our results specialise to any model for (∞, 1)-categories, therefore generalising results on quasi-categories and also categories.