Abstract In this paper, we show that the spectral mapping theorem holds for ( m , n ) * {(m,n)^{*}} -paranormal operators. We also exhibit the self-adjointness of the Riesz idempotent E λ {E_{\lambda}} of ( m , n ) * {(m,n)^{*}} -paranormal operators concerning for each isolated point λ of σ ( T ) {\sigma(T)} . Moreover, we show Weyl’s theorem for ( m , n ) * {(m,n)^{*}} -paranormal operators and f ( T ) {f(T)} for every f ∈ ℋ ( σ ( T ) ) {f\in\mathcal{H}(\sigma(T))} . Furthermore, we investigate the class of totally ( m , n ) * {(m,n)^{*}} -paranormal operators and show that Weyl’s theorem holds for operators in this class.