The article aims at investigating speech processing prerequisite claims made by Pienemann's Processability Theory (1998). Longitudinal data from eight English L1 and one French L1 speaker learning Arabic as an L2 were used to investigate the emergence/processing of demonstrative-predicate gender agreement and verbal agreement structures hypothesized to be processable at the same stage: Stage 4. The findings show that both forms were not processable by the English L1 participants at the same stage, as the participants seemed to encounter more problems with demonstrative-predicate agreement than with verbal agreement. The findings are further supported by cross-sectional data of 53 English and French L2 learners of Arabic, where between-group effects were found with respect to demonstrative-predicate agreement. It is concluded that this is likely due to L1 transfer--a factor not accounted for by Processability Theory.