The association of multiple Transcription Factors (TFs) in the cis‐regulatory region is imperative for developmental changes in eukaryotes. The underlying process is exceedingly complex, and it is not at all clear what orchestrates the overall search process by multiple TFs. In this study, by developing a theoretical model based on a discrete‐state stochastic approach, we investigated the target search mechanism of multiple TFs on nucleosomal DNA. Experimental kinetic rate constants of different TFs are taken as input to estimate the Mean‐First‐Passage time to recognize the binding motifs by two TFs on a dynamic nucleosome model. The theory systematically analyzes when the TFs search their binding motifs hierarchically and when simultaneously by proceeding via the formation of a protein‐protein complex. Our results, validated by extensive Monte Carlo simulations, elucidate the molecular basis of the complex target search phenomenon of multiple TFs on nucleosomal DNA.