Pines and Schrieffer demonstrated that the two‐stream instability could occur in a high‐mobility semiconductor such as InSb if the conditions &ohgr;p+&tgr;+>10 andT−»T+are satisfied, where &ohgr;p+is the hole‐plasma frequency, &tgr;+is the hole‐collision time andT−andT+are the electron and hole temperatures, respectively. Either condition is difficult to obtain in bulk InSb. The possibility of observing such an instability in a structure consisting of adjacentpandnInSb is considered. The collision condition is reconsidered using a collision term which conserves particles and assuming the somewhat higher electron‐drift velocities (≃electron‐thermal velocity) which are now believed possible. It is concluded that the condition can be relaxed by about an order of magnitude (&ohgr;p+&tgr;+>1). The layered structure could provide the conditionT+«T−if it were in contact with liquid helium while a current, passed only in thenregion, produced both relative streaming and elevated electron temperatures. A comparative stability analysis in the zero‐temperature fluid limit indicates that the surface space‐charge waves of the layered structure can grow at rates only slightly less than those of the bulk space‐charge waves of the corresponding penetrating stream system.