<p>This paper focuses on the problem of distributed online convex optimization with nonlinear switching costs in a multi-agent network. In this problem, each agent has its own time-varying private loss function, which is either convex or convex and smooth, and is restricted to partial access to information about the global time-varying loss functions. Consequently, agents need to engage in local information exchange with their neighbors to make decisions, and any changes in decisions will incur additional costs in a nonlinear manner. To address this problem, two algorithms are proposed: The distributed online gradient descent algorithm (DOGD) for general convex loss functions and the distributed online gradient tracking algorithm (DOGT) for convex and smooth loss functions. It is shown that both the proposed algorithms have sublinear dynamic regret bounds when the environment undergoes sublinear changes. In the end, a numerical simulation of a distributed online learning example is conducted to validate the theoretical results.</p>