This paper presents a new model for word alignment in statistical translation based on a first-order Hidden Markov Model (HMM). The model differs from traditional approaches by making alignment probabilities dependent on the relative positions of words rather than their absolute positions. This approach is inspired by HMMs used in speech recognition for time alignment, but without the monotonicity constraint on word order. The model is tested on several bilingual corpora, including the Avalanche Bulletins, Verbmobil Corpus, and Eu’Trans Corpus. The paper reviews the statistical translation model, which aims to translate a text from one language to another by selecting the most probable target sentence. The key challenge is defining the correspondence between words in the source and target languages. Two alignment models are described: a mixture-based model (IBM1) and an HMM-based model. The mixture-based model uses a uniform alignment probability, while the HMM-based model considers the relative position of words and uses dynamic programming for training. The HMM-based model is trained using maximum likelihood estimation and produces translation probabilities comparable to the mixture model. The model generates smoother position alignments, which is particularly useful for languages like German where compound words are aligned to multiple words in the source language. However, the model may struggle with large jumps in word positions due to different word orderings in the two languages. The paper also discusses the limitations of the HMM model and suggests possible extensions, such as incorporating multi-word phrases and part-of-speech tags. The results show that the HMM model performs well on the Avalanche and Verbmobil corpora, but the mixture model provides slightly better results for translation probabilities. The HMM model is considered more effective for aligning words in languages with complex structures, while the mixture model is better for handling large jumps in word positions. The study concludes that further research is needed to improve the HMM model for handling large jumps and to develop a multilevel HMM model that can handle a limited number of large jumps.This paper presents a new model for word alignment in statistical translation based on a first-order Hidden Markov Model (HMM). The model differs from traditional approaches by making alignment probabilities dependent on the relative positions of words rather than their absolute positions. This approach is inspired by HMMs used in speech recognition for time alignment, but without the monotonicity constraint on word order. The model is tested on several bilingual corpora, including the Avalanche Bulletins, Verbmobil Corpus, and Eu’Trans Corpus. The paper reviews the statistical translation model, which aims to translate a text from one language to another by selecting the most probable target sentence. The key challenge is defining the correspondence between words in the source and target languages. Two alignment models are described: a mixture-based model (IBM1) and an HMM-based model. The mixture-based model uses a uniform alignment probability, while the HMM-based model considers the relative position of words and uses dynamic programming for training. The HMM-based model is trained using maximum likelihood estimation and produces translation probabilities comparable to the mixture model. The model generates smoother position alignments, which is particularly useful for languages like German where compound words are aligned to multiple words in the source language. However, the model may struggle with large jumps in word positions due to different word orderings in the two languages. The paper also discusses the limitations of the HMM model and suggests possible extensions, such as incorporating multi-word phrases and part-of-speech tags. The results show that the HMM model performs well on the Avalanche and Verbmobil corpora, but the mixture model provides slightly better results for translation probabilities. The HMM model is considered more effective for aligning words in languages with complex structures, while the mixture model is better for handling large jumps in word positions. The study concludes that further research is needed to improve the HMM model for handling large jumps and to develop a multilevel HMM model that can handle a limited number of large jumps.