Established international soil classification systems have not properly accommodated acid sulfate soils (ASS) and soil materials in Finland and Sweden because: (1) in these soils some diagnostic ASS properties are too deep to meet the depth requirements, and (2) there is a lack of defined diagnostic soil classification criteria for acidic and potentially acidic soil materials that do not completely fulfill the diagnostic pH-criterion of pH < 4.0. In this paper, two new ASS materials are introduced with the prefix “para” for parasulfuric material (oxidized material) and parahypersulfidic material (reduced material). These materials have diagnostic pH-criteria of pH 4.0–4.5 and 3.0–3.5 (field-pH for parasulfuric material and incubation-pH for parahypersulfidic material) for mineral and organic soil materials (here defined as > 20% organic matter; peat and gyttja), respectively. The term “para-acid sulfate soil (para-ASS) material” is introduced for soil materials which may have a considerable environmental impact due to mobilization of acidity and dissolved metals. Because organic acids may lower pH to values below the established pH-value of < 4.0 for ASS materials, a pH of < 3.0 is used in the Finnish-Swedish ASS classification for organic soil materials. These changes and new additions to existing diagnostic ASS materials have consequently also led to a slight modification of the required field-pH values of the existing terms “hypersulfidic material” and “sulfuric material”. The Finnish-Swedish ASS classification further includes a systematic way for classification of the entire soil profile and no depth requirements for diagnostic ASS materials are present; what matters is the current or potential environmental impact that the soil has or may have. It is proposed that the Finnish-Swedish ASS classification may serve as a framework for establishing a unified ASS classification globally and that the new diagnostic ASS materials are included in relevant international soil classification systems.