It sounds like your tomatoes have a fungal disease; there are a number of fungi that commonly attack these plants.
Help slow or stop the disease's spread by plucking off the affected leaves. Make sure your tomatoes are in a spot with full sun. Prune or train them so they have good air circulation. Shade or stagnant air can encourage disease. Also avoid getting the foliage wet whenever possible, as wet leaves also encourage disease.
Do you fertilize your tomatoes? Too much fertilizer may make them more susceptible to disease, as well. So cutting back on the fertilizer may help.
Other than that, the best thing I can recommend is using a fungicide on your plants. Be sure to select one that's labeled for use on edible crops, and follow the directions on the packaging when you use it.