Johnson (1972) and Kaplan & Kay (1994) showed that phonological processes belong to the computational class of regular relations. This paper provides a computational analysis of long-distance consonant agreement and shows that it belongs to a more restricted computational class called subsequential. This paper further argues that subsequentiality is a desirable computational characterization of long-distance consonant agreement for the following reasons. First, it is sufficiently expressive. Second, it is restrictive as it accounts for the absence of pathological patterns like Majority Rules and Sour Grapes from the typology (Heinz & Lai 2013), standing in contrast to Agreement by Correspondence analysis in Optimality Theory (Rose & Walker 2004; Hansson 2007).