An electron microscope study of thin sections of interphase cells has revealed the following:- Circular pores are formed in the double nuclear envelope by continuities between the inner and outer membranes which permit contact between the nucleoplasm and the cytoplasm unmediated by a well defined membrane. The pores, seen in sections normal to the nuclear envelope, are profiles of the ring-shaped structures described by others and seen in tangential section. The inner and outer nuclear membranes are continuous with one another and enclose the perinuclear space. The pores contain a diffuse, faintly particulate material. A survey of cells of the rat derived from the embryonic ectoderm, mesoderm, and endoderm, and of a protozoan and an alga has revealed pores in all tissues examined, without exception. It is concluded that pores in the nuclear envelope are a fundamental feature of all resting cells. In certain cells, the outer nuclear membrane is continuous with membranes of the endoplasmic reticulum, hence the perinuclear space is continuous with cavities enclosed by those membranes. There are indications that this is true for all resting cells, at least in a transitory way. On the basis of these observations, the hypothesis is made that two pathways of exchange exist between the nucleus and the cytoplasm; by way of the perinuclear space and cavities of the endoplasmic reticulum and by way of the pores in the nuclear envelope.