The linear relaxation time (LRT) associated with steady-state correlation functions is studied for Langevin equations with non-Gaussian noises: dichotomous Markov noise and Poissonian white shot noise. Exact results for arbitrary models are obtained and compared with results for Gaussian noises. Some general features of LRTs are discussed. The concept of dynamic effective diffusion is introduced and the existence of an optimal effective Fokker-Planck approximation is discussed. Explicit examples for prototype models are presented and briefly compared with the analogs for Gaussian noises.