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In this paper, we study two classes of quasi-double diagonally dominant tensors and prove they are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>-tensors. Numerical examples show that two classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>-tensors are mutually exclusive. Thus, we extend the decision conditions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>-tensors. Based on these two classes of tensors, two estimation inequalities for the upper and lower bounds for the spectral radius of nonnegative tensors are obtained.