We propose kernel ridge regression estimators for causal inference in multistage settings. Specifically, we focus on (i) the decomposition of a total effect into a direct effect and an indirect effect (mediated by a particular mechanism); and (ii) effects of sequences of treatments. We allow treatment, covariates, and mediators to be discrete or continuous, and low, high, or infinite dimensional. We propose estimators of means, increments, and distributions of counterfactual outcomes. Important examples are (i) direct and indirect dose response curves; and (ii) dynamic dose response curves. Each estimator has a closed form solution and is easily computed by kernel matrix operations. For the nonparametric case, we prove uniform consistency and provide finite sample rates of convergence. For the semiparametric case, we prove root-n consistency, Gaussian approximation, and semiparametric efficiency. We evaluate our estimators in simulations then estimate mediated and dynamic treatment effects of the US Job Corps training program for disadvantaged youth.