In this study, measurement invariance and differential item functioning (DIF) studies of the TIMSS 2019 4^th and 8th-grade mathematics and science achievement tests were conducted for the country groups participating in both TIMSS and eTIMSS. The study sample consisted of 9560 responders of the first booklet of the 2019 cycle. Multiple Group Confirmatory Factor Analysis (MGCFA) was utilized to test measurement invariance, and Mantel-Haenszel (MH), Logistic Regression (LR), and SIBTEST were used for the DIF analyses. The measurement invariance results indicated strict invariance between groups for all tests which included 111 items in total. In the DIF analyses, for the 4^th and 8^th-grade mathematics tests, only three items showed moderate DIF with MH, and four items showed DIF with SIBTEST. For the 4^th-grade science test, one item showed moderate DIF with both MH and SIBTEST. However, in the 8^th-grade science test, no items showed DIF with MH and LR methods, while four items showed moderate DIF with SIBTEST. Overall, MH and SIBTEST techniques were in agreement, whereas LR method produced inconsistent results and showed disagreement with these two methods. The results of the measurement invariance analysis and the LR method were consistent and indicated equivalency of TIMSS and e-TIMSS scores.