Recent experimental results on nonleptonic hyperon decays are studied on the basis of a doublet approximation for strong and weak interactions, with the implied suggestion that this higher symmetry may be more easily discernable in such reactions in which $K$-particles do not occur explicitly. The doublet approximation is characterized by a doublet spin $I$ which is equal to \textonehalf{}, 1, 0 for baryons, $\ensuremath{\pi}$, $K$, respectively and by a $K$ spin. It is not necessary to assume that the strong $K$ interactions are weak compared to the strong $\ensuremath{\pi}$ interactions. For the mentioned reactions it is necessary to assume that the strong interactions which do not conserve $I$ play a minor role compared to those which conserve $I$.The following refinement of the nonleptonic $\ensuremath{\Delta}T=\frac{1}{2}$ rule is proposed. ($T=\mathrm{isotopic}\mathrm{spin}$). The weak nonleptonic interactions consist of two parts ${H}^{(0)}$, ${H}^{(1)}$ with $\ensuremath{\Delta}I=0, 1$, respectively. In the doublet approximation ${H}^{(0)}$ and ${H}^{(1)}$ separately conserve parity in the presence of all strong $\ensuremath{\pi}$ and $K$ interactions. ${H}^{(0)}$ and ${H}^{(1)}$ together do not conserve parity, however. In addition to $\ensuremath{\Delta}I=1$, ${H}^{(1)}$ should in general satisfy a further constraint, but there are classes of graphs for which $\ensuremath{\Delta}I=1$ is sufficient.Current X current structures for ${H}^{(0)}$ and ${H}^{(1)}$ are examined. Results of an earlier paper can be viewed as a special case of the $\ensuremath{\Delta}I=0,1$ rule. The same is true for results obtained by Feldman, Matthews, and Salam and by Wolfenstein. The considerations of these authors can be extended to wider classes of graphs.Odd relative helicity and the relation between rates for $\ensuremath{\Lambda}\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{\ensuremath{-}}$, ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{0}$ are consequences of the $\ensuremath{\Delta}I=0, 1$ rule only. So is the prediction that $\ensuremath{\Xi}$ decay is strongly $P$ nonconserving.The parity properties of ${H}^{(0)}$, ${H}^{(1)}$ are sufficient conditions. It is a delicate question whether they are necessary. For a subset of graphs they are not necessary, but this set seems arbitrary. If it is assumed that the parity conditions are necessary, the schizon scheme is ruled out.It is noted that the nonleptonic weak interactions may be generated by the strong interactions in terms of the following prescription. ${H}^{(1)}$ is generated by assuming that the $\ensuremath{\pi}(K)$ fields have small $K(\ensuremath{\pi})$ components. An ${H}^{(0)}$ is generated by assuming that the doublets ${N}_{1}({N}_{2})$ have small ${N}_{2}({N}_{1})$ components; likewise for ${N}_{3}$ and ${N}_{4}$. Further, it is observed that one can construct a non-electromagnetic $\ensuremath{\Delta}T=\frac{3}{2}$ interaction which is small in the sense that it only contributes to ${{K}_{\ensuremath{\pi}2}}^{+}$ to the extent that the doublet approximation is not valid.