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Mints, such as Spearmint (Mentha spicata) can get various fungal maladies such as leaf spots and anthracnose. Most of these only cause slight damage, but to reduce incidence, remove blighted leaves and try to give you plant slightly drier conditions and more light and air circulation. The damage appears minor and will hopefully remain so. It is hard to identify at this stage, especially without better photographs. Some of the numerous pathogens that can affect Mentha are Mint Anthracnose (Sphaceloma menthae), Mint Leaf Spots (Ramularia menthicola, Septoria menthae), Mint Rust (Puccinia menthae) and Mint Blight (Cephalosporium sp.)