We predict several new exotic doubly heavy hadronic resonances, inferring from the observed exotic bottomoniumlike and charmoniumlike narrow states X(3872), Z_{b}(10610), Z_{b}(10650), Z_{c}(3900), and Z_{c}(4020/4025). We interpret the binding mechanism as mostly molecularlike isospin-exchange attraction between two heavy-light mesons in a relative S-wave state. We then generalize it to other systems containing two heavy hadrons which can couple through isospin exchange. The new predicted states include resonances in meson-meson, meson-baryon, baryon-baryon, and baryon-antibaryon channels. These include those giving rise to final states involving a heavy quark Q=c,b and antiquark Q[over ¯]^{'}=c[over ¯],b[over ¯], namely, DD[over ¯]^{*}, D^{*}D[over ¯]^{*}, D^{*}B^{*}, B[over ¯]B^{*}, B[over ¯]^{*}B^{*}, Σ_{c}D[over ¯]^{*}, Σ_{c}B^{*}, Σ_{b}D[over ¯]^{*}, Σ_{b}B^{*}, Σ_{c}Σ[over ¯]_{c}, Σ_{c}Λ[over ¯]_{c}, Σ_{c}Λ[over ¯]_{b}, Σ_{b}Σ[over ¯]_{b}, Σ_{b}Λ[over ¯]_{b}, and Σ_{b}Λ[over ¯]_{c}, as well as corresponding S-wave states giving rise to QQ^{'} or Q[over ¯]Q[over ¯]^{'}.