<p>Continuous state nonhomogeneous Markov chains are widely used to model the performance of random variables continuously varied over time in many fields such as population biology. Existing works mainly focus on their strong law of large numbers. There is little work developed on their limit theorems. To this end, this paper investigates the limiting properties of continuous state nonhomogeneous Markov chains, and establishes limit theorems for multivariate functions of continuous state nonhomogeneous Markov chains, including the strong law of lager numbers, the central limit theorem and almost sure central limit theorem under some mild conditions, which are some basic theoretical properties for statistical inference and predictions of continuous-time-varying random variables.</p>