This study examined the relationship between the Collegiate Assessment of Academic Proficiency Critical Thinking test (CAAP-CT) and the College Outcome Measures Program objective test battery (COMP). Focus was on determining: (1) the relationship between the CAAP-CT and the COMP process-oriented subscores and the freshman to sophomore gains in these subscores; and (2) at a composite score level, the relationship of the CAAP-CT score with the COMP total, COMP total gain, entering American College Testing (ACT) Program composite score, and cumulative grade point average. A secondary objective was to determine whether or not a test order effect exists within an approximately 3.5-hour testing session, by comparing those who took the CAAP-CT followed by the COMP with those who took the COMP followed by the CAAP-CT. Data were obtained at Northeast Missouri State University (Kirksville) from students taking their required sophomore examinations during the fall of 1988 and the spring of 1989. The data set analyzed contained valid observations for 568 students. Results indicate that the order in which students took the COMP and CAAP-CT had no significant impact on the score results. There are significant zero-order correlations between COMP process-oriented subscores and CAAP-CT scores. The COMP-based process subscores account for at least 33% of the variance in CT and up to 40% with COMP-based gain scores included. There was insufficient evidence to support the contention that higher gains are associated with higher levels of CT. The ACT maintained a greater relationship to the CAAP-CT than did the COMP, which was administered at the same time and offers more tasks requiring CT skills. Twenty-three data tables are included. (RLC)