Most cytoplasmic-replicating negative-strand RNA viruses (NSVs) initiate genome transcription by cap snatching. The source of host mRNAs from which the cytoplasmic NSVs snatch capped-RNA leader sequences has remained elusive. Earlier reports have pointed towards cytoplasmic-RNA processing bodies (P body, PB), although several questions have remained unsolved. Here, the nucleocapsid (N) protein of plant- and animal-infecting members of the order Bunyavirales, in casu Tomato spotted wilt virus (TSWV), Rice stripe virus (RSV), Sin nombre virus (SNV), Crimean-Congo hemorrhagic fever virus (CCHFV) and Schmallenberg virus (SBV) have been expressed and localized in cells of their respective plant and animal hosts. All N proteins localized to PBs as well as stress granules (SGs), but extensively to docking stages of PB and SG. TSWV and RSV N proteins also co-localized with Ran GTPase-activating protein 2 (RanGAP2), a nucleo-cytoplasmic shuttling factor, in the perinuclear region, and partly in the nucleus when co-expressed with its WPP domain containing a nuclear-localization signal. Upon silencing of PB and SG components individually or concomitantly, replication levels of a TSWV minireplicon, as measured by the expression of a GFP reporter gene, ranged from a 30% reduction to a four-fold increase. Upon the silencing of RanGAP homologs in planta, replication of the TSWV minireplicon was reduced by 75%. During in vivo cap-donor competition experiments, TSWV used transcripts destined to PB and SG, but also functional transcripts engaged in translation. Altogether, the results implicate a more complex situation in which, besides PB, additional cytoplasmic sources are used during transcription/cap snatching of cytoplasmic-replicating and segmented NSVs.