This paper describes continuous carry-over fMRI experiments. In these studies, stimuli are presented in an unbroken, sequential manner, and can be used to estimate simultaneously the mean difference in neural activity between stimuli as well as the effect of one stimulus upon another (carry-over effects). Neural adaptation, which has been the basis of many recent fMRI studies, is shown to be a specific form of carry-over effect. With this approach, the adapting effects of stimuli may be studied in a continuous sequence, as opposed to within isolated pairs or blocks. Additionally, the average, direct effect of a stimulus upon neural response can form the basis of a simultaneously obtained distributed pattern analysis, allowing comparison of neural population coding on focal (within voxel) and distributed (across voxel) spatial scales. These studies are ideally conducted with serially balanced sequences, in which every stimulus precedes and follows every other stimulus. While m-sequences can provide this stimulus order, the type 1 index 1 sequence of Finney and Outhwaite may be used in fMRI studies for those experimental designs for which an m-sequence solution does not exist. Continuous carry-over designs with serially balanced sequences are argued to be particularly well suited to the characterization of "similarity spaces," in which the perceptual similarity of stimuli is related to the structure of neural representation both within and across voxels. These concepts are illustrated with a worked example involving the neural representation of color. It is shown that data from a single scanning session are sufficient to detect direct and carry-over effects, as well as demonstrate the correspondence of the similarity structure of distributed patterns of neural firing and the perceptual similarity of a set of colors.