We study the question of whether local incentive constraints are sufficient to imply full incentive compatibility in a variety of mechanism design settings, allowing for probabilistic mechanisms. We give a unified approach that covers both continuous and discrete type spaces. On many common preference domains—including any convex domain of cardinal or ordinal preferences, single‐peaked ordinal preferences, and successive single‐crossing ordinal preferences—local incentive compatibility (suitably defined) implies full incentive compatibility. On domains of cardinal preferences that satisfy a strong nonconvexity condition, local incentive compatibility is not sufficient. Our sufficiency results hold for dominant‐strategy and Bayesian Nash solution concepts, and allow for some interdependence in preferences.