This thesis explores how task parallelness might be established; this is of fundamental importance to any discussion in the areas of language testing and task-based research, where the equivalence of tasks is a prerequisite. Five pilot studies were conducted using two spoken narrative tasks from an ongoing speaking test of English in Japan, the Standard Speaking Test, including two feasibility studies using several linguistic variables to analyse candidate performances, a study of expert judgements of the two tasks, a study of the linguistic performance of native speakers of English, and a study to identify an appropriate pair of tasks for the main study. The main study examined the parallelness of two spoken narrative tasks by Hill (1960) in terms of the ratings calculated by MFRM analysis, the linguistic performances of 65 Japanese candidates and 11 native speakers of English, expert judgements by Japanese teachers of English, and perceptions of the Japanese candidates and native speakers of English. The validity of the linguistic variables was also examined. The results of analyses demonstrated that the two tasks were not actually parallel, despite the effort to ensure a priori parallelness via the pilot studies. The findings were extensively discussed in relation to the theories of task complexity from Robinson (2001) and Skehan (1998), and raised several questions regarding the variables for quantifying the accuracy and syntactic complexity of linguistic performance. Taken together, the findings of this thesis add significantly to the understanding of task parallelness and the results of my work can be applied not only to the design and selection of tasks but also to the investigation of linguistic performance in the fields of language testing and task-based research.