Answer: Unfortunately it sounds like your plants are suffering from early blight. Pick off the affected leaves and destroy them immediately as they appear on the plants to try to slow its spread; then keep the plants growing as vigorously as you can. (If you can keep enough healthy leaves on the plant you may be able to save some of the crop.)
Be sure they have adequate nutrients and water, but avoid overhead watering. Next, some gardeners apply a foliar spray of compost tea* every two to three weeks, others treat this with a copper based fungicide according to the label instructions.
Early blight can blow in on the wind or can overwinter on tomato plant debris including the vines, leaves and even seeds, so remove and destroy any tomato plant debris. In the future, try to choose varieties with flat, uncurled leaves, which are less susceptible to fungal infection because they dry more quickly after a rain. Also, plant your tomatoes in a new location every year on a three year rotation or more, being careful to keep them away from potatoes and places potatoes have grown since they are both affected by early blight.
*You can make the tea by adding 1 part aged compost that contains some manure to 5 parts water and letting the mixture sit in the shade for 2 weeks. Then strain through cheesecloth and spray the liquid on your plants. The tea contains fungi that outcompete the blight fungi.
Good luck with your tomatoes.
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