This paper introduces a probabilistic model called a covariance model (CM) for RNA sequence analysis. The model captures both the secondary structure and primary sequence consensus of an RNA family. It is particularly effective for searching for tRNA sequences in databases. The model can be built automatically from existing sequence alignments or even from unaligned sequences. The CM is trained using an iterative process that combines comparative sequence analysis with an algorithm for RNA secondary structure prediction based on pairwise covariances in multiple alignments. The CM is used for consensus secondary structure prediction, multiple sequence alignment, and database similarity searching. A dynamic programming algorithm is described for efficiently finding the globally optimal alignments of RNA sequences to a model. The algorithm is used for database searching and is efficient, with a time complexity of O(N³M) and memory complexity of O(N²M). The CM is tested on tRNA sequences and shows significantly higher sensitivity than existing tRNA searching programs. The CM is also used for multiple sequence alignment, which is a prerequisite for phylogenetic tree inference and RNA structure prediction. The CM can be trained from unaligned sequences, allowing for the prediction of consensus secondary structure. The model is shown to produce accurate alignments and correctly predict the consensus secondary structure of tRNA sequences. The CM is a generalization of hidden Markov models (HMMs) and is used for RNA sequence analysis. It is particularly effective for RNA sequences where secondary structure is more important than primary sequence conservation. The CM is shown to capture both primary and secondary structure consensus information while flexibly scoring insertions, deletions, and mismatches. The CM is also used for database searching, where it is compared to existing tRNA detection programs. The CM is shown to be more sensitive and accurate than existing programs. The CM is also used for searching for tRNA genes in the genome of Podospora anserina, where it detects all 27 tRNA genes with no false positives. The CM is a powerful tool for RNA sequence analysis, allowing for the prediction of consensus secondary structure and multiple sequence alignment. It is particularly useful for RNA sequences where secondary structure is more important than primary sequence conservation. The CM is a generalization of HMMs and is used for RNA sequence analysis. It is particularly effective for RNA sequences where secondary structure is more important than primary sequence conservation. The CM is a powerful tool for RNA sequence analysis, allowing for the prediction of consensus secondary structure and multiple sequence alignment. It is particularly useful for RNA sequences where secondary structure is more important than primary sequence conservation.This paper introduces a probabilistic model called a covariance model (CM) for RNA sequence analysis. The model captures both the secondary structure and primary sequence consensus of an RNA family. It is particularly effective for searching for tRNA sequences in databases. The model can be built automatically from existing sequence alignments or even from unaligned sequences. The CM is trained using an iterative process that combines comparative sequence analysis with an algorithm for RNA secondary structure prediction based on pairwise covariances in multiple alignments. The CM is used for consensus secondary structure prediction, multiple sequence alignment, and database similarity searching. A dynamic programming algorithm is described for efficiently finding the globally optimal alignments of RNA sequences to a model. The algorithm is used for database searching and is efficient, with a time complexity of O(N³M) and memory complexity of O(N²M). The CM is tested on tRNA sequences and shows significantly higher sensitivity than existing tRNA searching programs. The CM is also used for multiple sequence alignment, which is a prerequisite for phylogenetic tree inference and RNA structure prediction. The CM can be trained from unaligned sequences, allowing for the prediction of consensus secondary structure. The model is shown to produce accurate alignments and correctly predict the consensus secondary structure of tRNA sequences. The CM is a generalization of hidden Markov models (HMMs) and is used for RNA sequence analysis. It is particularly effective for RNA sequences where secondary structure is more important than primary sequence conservation. The CM is shown to capture both primary and secondary structure consensus information while flexibly scoring insertions, deletions, and mismatches. The CM is also used for database searching, where it is compared to existing tRNA detection programs. The CM is shown to be more sensitive and accurate than existing programs. The CM is also used for searching for tRNA genes in the genome of Podospora anserina, where it detects all 27 tRNA genes with no false positives. The CM is a powerful tool for RNA sequence analysis, allowing for the prediction of consensus secondary structure and multiple sequence alignment. It is particularly useful for RNA sequences where secondary structure is more important than primary sequence conservation. The CM is a generalization of HMMs and is used for RNA sequence analysis. It is particularly effective for RNA sequences where secondary structure is more important than primary sequence conservation. The CM is a powerful tool for RNA sequence analysis, allowing for the prediction of consensus secondary structure and multiple sequence alignment. It is particularly useful for RNA sequences where secondary structure is more important than primary sequence conservation.