The foreign exchange (forex) market is a dynamic and complex financial arena where the exchange rates of various currency pairs fluctuate continuously. Among these currency pairs, EUR/TRY and USD/TRY hold significant economic relevance due to their roles in international trade and finance. In this study, we analyze the multifractality of hourly EUR/TRY and USD/TRY exchange rate data for the whole period, as well as its time-varying individual and cross correlations, spanning from May 31, 2018, to March 21, 2022. We employ multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal detrended fluctuation analysis (MF-DFA) methodologies. The aim of studying multifractality in exchange rates is to comprehend and model the complex and intricate nature of price movements and dynamics of the EUR/TRY and USD/TRY exchange rates. In the analysis of the whole period, multifractality is detected in individual exchange rates and cross correlations. In the rolling window analysis, we demonstrated how multifractality and cross correlation multifractality change over time. Additionally, contributions of the sources of the multifractality are investigated in a time-varying framework. Multifractal nature of these exchange rates indicate that they exhibit complex and scale-dependent behaviors, which go beyond the traditional linear models. The existence of multifractality in EUR/TRY and USD/TRY exchange rates has significant implications for financial modeling, risk management, and trading strategies. It implies that standard linear models may not capture the full complexity of these markets, necessitating the development of more sophisticated models that account for multifractal properties. [ABSTRACT FROM AUTHOR]