Abstract Agglomerative clustering methods with stopping criteria are generalized. Clustering-related concepts are rigorously formulated with special consideration on metricity of object space. A new definition of combinatoriality is given, and a stronger proposition of monotonicity is proven. Specializations of the general method are applied to non-attributive non-metric and attributive pseudometric representations of biosequences. The furthest neighbor method is shown suitable for non-metric use. In metric object space, four inter-clusteral distance functions, including a new truly context sensitive method, are compared using a method-independent goodness criterion. For biosequence clustering, the new method overcomes the UPGMA, UPGMC, and furthest neighbor methods.