Answer: From your description, it sounds like your plants could be affected by one of three common tomato blights. Septoria leaf spot (or blight) and Early Blight are the two most common, both of which tend to start after the fruit sets. The third is Late Blight, which usually only occurs after unusually cool, wet weather. These are all airborne fungal diseases that require dew or rain to infect the plants. These diseases build up rapidly in wet weather and cause dark leaf spots followed by yellowing and defoliation (leaf drop). They may also produce spots on the fruit.
You can try cutting off the affected foliage, however these blights are difficult to control once established. This fall, pull up and destroy any remaining vines. Because this fungus can over winter in the soil, rotate your tomato plantings every year (plant in the same place only once every 4 years) Mulch the base of the plants with 1-2 inches of straw, newspaper or other organic materials and water the plants from the bottom. Consider spacing the plants further apart to increase air circulation and use a fungicide as needed.
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