What cognitive processes underlie event-related brain potential (ERP) effects related to visual multidimensional selective attention and how are these processes organized? We recorded ERPs when participants attended to one conjunction of color, global shape and local shape and ignored other conjunctions of these attributes in three discriminability conditions. Attending to color and shape produced three ERP effects: frontal selection positivity (FSP), central negativity (N2b), and posterior selection negativity (SN). The results suggested that the processes underlying SN and N2b perform independent within-dimension selections, whereas the process underlying the FSP performs hierarchical between-dimension selections. At posterior electrodes, manipulation of discriminability changed the ERPs to the relevant but not to the irrelevant stimuli, suggesting that the SN does not concern the selection process itself but rather a cognitive process initiated after selection is finished. Other findings suggested that selection of multiple visual attributes occurs in parallel.