Summary: For \(0<p<1\), the class of \(p\)-\(w\)-hyponormal operators is introduced. This class contains all \(w\)-hyponormal operators. Certain properties of this class of operators are obtained. First, many properties that the \(w\)-hyponormal operators possess are shown to hold for the \(p\)-\(w\)-hyponormal operators; for example, if \(T\) is a \(p\)-\(w\)-hyponormal operator, then its spectral radius and norm are identical, and the nonzero points of its joint point spectum and point spectum are identical. Secondly, for some special \(p\)-\(w\)-hyponormal operators, we also prove that their squares are \(p\)-\(w\)-hyponormal operators; but in general, it is not true for all \(p\)-\(w\)-hyponormal operators. Lastly, we show that there is no \(p\)-\(w\)-hyponormal operator in an \(n\)-dimensional space unless it is a normal operator.