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<p/> <p>By using Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least <inline-formula><graphic file="1687-1847-2010-262461-i3.gif"/></inline-formula> positive periodic solutions for <inline-formula><graphic file="1687-1847-2010-262461-i4.gif"/></inline-formula>-species nonautonomous Lotka-Volterra type food chains with harvesting terms. An example is given to illustrate the effectiveness of our results.</p>