found oil in radiator and coolant overflow ??? on 1990 Cadillac DeVille

Car runs fine with just a small hint of maybe a skip. Checked radiator and overflow and found what seems to be oil in both. Car seemed to be burning lots of fuel during usage. Thought of head gasket but exhaust seems to be o.k. NO SMOKE.
Any suggestions??? 1990 Sedan DeVille

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2 answers
HAVE TRANS. COOLER TESTED, IT IS PART OF THE RADIATOR.
this could be one of several issue car needs to be diag