Persons with stroke-induced aphasia (PWAs) are often impaired in tense/time reference (TR) production. It is not clear, however, whether PWAs’ impaired TR production is due to TR-related encoding or retrieval deficits. This study aims at disentangling TR-related encoding deficits from TR-related retrieval deficits in aphasia. Two sentence completion tasks (SCTs) tapping production of past and future reference were administered to eight Greek-speaking PWAs, eight Russian-speaking PWAs, six Italian-speaking PWAs, seven English-speaking PWAs and four groups of language-, age- and education-matched healthy controls. SCT 1 tapped TR-related encoding processes and TR-related retrieval processes to a similar extent. SCT 2 predominantly tapped TR-related retrieval processes. All four control groups performed at ceiling. Three Greek-speaking PWAs, one Russian-speaking PWA, three Italian-speaking PWAs and two English-speaking PWAs showed between-task dissociations. A double dissociation emerged, as some Greek-, Russian- and English-speaking PWAs performed better on SCT 1 than on SCT 2, whereas other Greek- and Italian-speaking PWAs performed worse on SCT 1 than on SCT 2. It will be shown that the experimental design employed here has the potential to disentangle TR-related encoding deficits from TR-related retrieval deficits, as both PWAs with selective TR-related encoding deficits and PWAs with selective TR-related retrieval deficits were identified.