This paper introduces, analyzes, and demonstrates a recursive hierarchical generalization of the widely used hidden Markov models, called Hierarchical Hidden Markov Models (HHMMs). The model is motivated by the complex multi-scale structure found in natural sequences, particularly in language, handwriting, and speech. The goal is to develop a systematic unsupervised approach for modeling such structures. By extending the standard Baum-Welch (forward-backward) algorithm, an efficient procedure is derived for estimating the model parameters from unlabeled data. The trained model is then used for automatic hierarchical parsing of observation sequences. The paper describes two applications of the model. In the first, it shows how to construct hierarchical models of natural English text, where different levels of the hierarchy correspond to structures on different length scales. In the second, it demonstrates how HHMMs can be used to automatically identify repeated strokes that represent combinations of letters in cursive handwriting. HHMMs are structured multi-level stochastic processes. Each state in an HHMM can be an autonomous probabilistic model, and the states emit sequences rather than single symbols. The model generates sequences through recursive activation of substates. This process ends when a production state is reached, which emits output symbols. Internal states do not emit observable symbols directly and are called internal states. The activation of a substate by an internal state is a vertical transition, while a horizontal transition occurs within the same level. The paper presents the estimation procedure for the parameters of HHMMs, which is inspired by the inside-outside algorithm. The structure of the model is general and allows an arbitrary number of activations of its submodels. The estimation procedure can be efficiently approximated, resulting in a quadratic time complexity in the length of the observations. This allows the model to capture long time correlations while keeping the running time reasonable. The paper also discusses the application of HHMMs to the modeling of natural English text, where the model exhibits the formation of "temporal experts" of different time scales, such as punctuation marks, frequent letter combinations, and phrase endings. Additionally, the model is used for unsupervised learning of repeated strokes in cursive handwriting. The paper is organized into sections that describe the model, its estimation procedure, two applications, and related work. The technical details are deferred to the appendices. The paper concludes that HHMMs provide a partial answer to two fundamental problems in complex sequence modeling: correlating structures occurring far apart in observation sequences and handling statistical inhomogeneities common in speech, natural language, and other complex sequences. The paper also discusses possible generalizations of HHMMs and their potential applications in various domains.This paper introduces, analyzes, and demonstrates a recursive hierarchical generalization of the widely used hidden Markov models, called Hierarchical Hidden Markov Models (HHMMs). The model is motivated by the complex multi-scale structure found in natural sequences, particularly in language, handwriting, and speech. The goal is to develop a systematic unsupervised approach for modeling such structures. By extending the standard Baum-Welch (forward-backward) algorithm, an efficient procedure is derived for estimating the model parameters from unlabeled data. The trained model is then used for automatic hierarchical parsing of observation sequences. The paper describes two applications of the model. In the first, it shows how to construct hierarchical models of natural English text, where different levels of the hierarchy correspond to structures on different length scales. In the second, it demonstrates how HHMMs can be used to automatically identify repeated strokes that represent combinations of letters in cursive handwriting. HHMMs are structured multi-level stochastic processes. Each state in an HHMM can be an autonomous probabilistic model, and the states emit sequences rather than single symbols. The model generates sequences through recursive activation of substates. This process ends when a production state is reached, which emits output symbols. Internal states do not emit observable symbols directly and are called internal states. The activation of a substate by an internal state is a vertical transition, while a horizontal transition occurs within the same level. The paper presents the estimation procedure for the parameters of HHMMs, which is inspired by the inside-outside algorithm. The structure of the model is general and allows an arbitrary number of activations of its submodels. The estimation procedure can be efficiently approximated, resulting in a quadratic time complexity in the length of the observations. This allows the model to capture long time correlations while keeping the running time reasonable. The paper also discusses the application of HHMMs to the modeling of natural English text, where the model exhibits the formation of "temporal experts" of different time scales, such as punctuation marks, frequent letter combinations, and phrase endings. Additionally, the model is used for unsupervised learning of repeated strokes in cursive handwriting. The paper is organized into sections that describe the model, its estimation procedure, two applications, and related work. The technical details are deferred to the appendices. The paper concludes that HHMMs provide a partial answer to two fundamental problems in complex sequence modeling: correlating structures occurring far apart in observation sequences and handling statistical inhomogeneities common in speech, natural language, and other complex sequences. The paper also discusses possible generalizations of HHMMs and their potential applications in various domains.