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In this paper, we consider the wild nonabelian Hodge correspondence forprincipal $G$-bundles on curves, where $G$ is a connected complex reductivegroup. We establish the correspondence under a ``very good" conditionintroduced by Boalch, and thus confirm one of his conjectures. We first give aversion of Kobayashi--Hitchin correspondence, which induces a one-to-onecorrespondence between stable meromorphic parahoric Higgs torsors of degreezero (Dolbeault side) and stable meromorphic parahoric connections of degreezero (de Rham side). Then, by introducing a notion of stability condition onfiltered Stokes local systems, we prove a one-to-one correspondence betweenstable meromorphic parahoric connections of degree zero (de Rham side) andstable filtered Stokes $G$-local systems of degree zero (Betti side). When$G={\rm GL}_n(\mathbb{C})$, the main result in this paper reduces toBiquad--Boalch's result.

Meromorphic Parahoric Higgs Torsors and Filtered Stokes G-local Systems on Curves