Starting from recent experiments in non-ionic surfactants, we discuss various topics characteristic of low rigidityK1materials. (1) The stability of the lamellar and cubic phases is studied in a simple model involvingK2the saddle-splay constantK2, and entropy terms due to the chains. We expect the lamellar phase to have a large range of existence, and the cubic phase to be of small extent. (2) We compare to cubic phases stability in largeK1materials. We discuss the mobility of edge dislocations on the basis of a new model of the core which involves stretching of the core layers in one dimension, and easy nucleation of pores in this region. The core extension is a characteristic length of lowK1materials which is much larger than de Gennes' length for microemulsions with a similar lowK1.