Multi-lingual handwriting means the script written with more than one language. In this paper, a hierarchical hidden Markov model network-based approach is proposed for on-line recognition of multi-lingual cursive handwritings. Basic characters of language, language network, and intermixed use of language are modeled with hierarchical relations. Since recognition corresponds to finding an optimal path in such a network, recognition candidates of each language are combined with probability without special treatment. Character labels of handwriting, language modes, and segmentation are obtained simultaneously. However, several difficulties caused by multiple language occurred during recognition. Applied heuristic methods are Markov chain for language mode transitions, pairwise discrimination for confusing pairs, and constrained routines for side effects by language related preprocessing methods. In spite of the addition of other language, recognition accuracy of each language drops negligibly on experimental results of multi-lingual with Hangul, English, and Digit case.