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Well, assuming this is not a trick question, those unsightly brown stains mean that your block or poured concrete walls have acid damage. (This has nothing to do with their having been poured in the sixties.) In this case, the clay's the thing, (as Shakespeare didn't say.) The clay outside your home is very acidic, so when the water leaks into your basement, the acidity comes along for the ride. Under normal circumstances, your basement wall acts as a filter, holding this acid back and allowing the "clean" water into your basement. Over time, acid damage will cause lower wall deterioration. If you notice signs of your walls being on an acid trip, call a local waterproofing professional for an intervention and treatment.