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The definition of a Detour&#8315;Harary index is <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#969;</mi> <mi>H</mi> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mo>&#8721;</mo> <mrow> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>&#8712;</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math> </inline-formula><inline-formula> <math display="inline"> <semantics> <mfrac> <mn>1</mn> <mrow> <mi>l</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">|</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </semantics> </math> </inline-formula>, where <i>G</i> is a simple and connected graph, and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>l</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">|</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> is equal to the length of the longest path between vertices <i>u</i> and <i>v</i>. In this paper, we obtained the maximum Detour&#8315;Harary index about unicyclic graphs, bicyclic graphs, and cacti, respectively.