This study investigated the constraints on the acquisition of the English progressive marking by Kiswahili EFL learners. Specifically, it examined lexical aspect and progressive meaning as factors constraining the acquisition of the English progressive marking by Tanzanian EFL learners. The participants in the study were 70 Form Two and Form Four students who were native speakers of Kiswahili. The data were collected by using a cloze-test designed to examine the association of the progressive marking with a full range of verb semantic features and progressive meaning. The data were coded and analyzed using inferential and descriptive statistics. The findings indicated limited effect of lexical aspect on the acquisition of the English progressive marking: progressive marking is strongly associated with activity verbs, but the spread of the progressive form was from activity > stative > achievement > accomplishment and there was incorrect overextension of the progressive form to stative verbs which decreased with increase in proficiency. The findings also provided evidence of the effects of progressive meaning: progressive marking appeared to be strongly associated with the meaning of in-progress and incompleteness and gradually extended to the meanings of temporariness, repetitiveness and preliminary stage. It was concluded that lexical aspect and the semantic meaning of the progressive aspect constrain L2 acquisition of the English progressive aspect marginally. Further research on the effect of lexical aspect and progressive meaning on L2 acquisition of the progressive marking involving participants from different proficiency levels is recommended.