We study subdirect products of free and Demushkin pro-p groups of depth infinity developing theory similar to the abstract case, see Bridson et al. (2002) [4]. Furthermore we classify when a subdirect product has homological type FP(m) for some m >= 2, a problem still open for abstract groups for m >= 3. (C) 2011 Elsevier Inc. All rights reserved.3431160172