Freeze-fracture electron microscopy is used to study the rippled texture in pure dimyristoyl and dipalmitoyl phosphatidylcholine membranes and in mixtures of dimyristoyl phosphatidylcholine and cholesterol. Evidence is presented that the apparent phase transition properties of multilamellar liposomes may be dependent on the manner in which liposomes are prepared. Under certain conditions the ripple structures as visualized by freeze-fracture electron microscopy for the pure phosphatidylcholines are observed to be temperature dependent in the vicinity of the pretransition. Thus the transition can sometimes appear to be a gradual transition rather than a sharp, first-order phase transition. In mixtures of dimyristoyl phosphatidylcholine and cholesterol, the ripple repeat distance is found to increase as the cholesterol concentration is increased between 0 and 20 mol%. Above 20 mol%, no rippling is observed. A simple theory is presented for the dependence of ripple repeat spacing on cholesterol concentration in the range 0--20 mol%. This theory accounts for the otherwise inexplicable abrupt increase in the lateral diffusion coefficients of fluorescent lipids in binary mixtures of phosphatidylcholine and cholesterol when the cholesterol concentration is increased above 20 mol%.