All cells receive and respond to signals from their environment, whether they live freely or are part of a tissue. Feedback loops are one among the interactions in signal-transduction cascades, in which the information from the downstream components is sent back to the upstream components of the system. Crosstalks between signal-transduction cascades are able to combine the information's received and processed to trigger the appropriate response. To understand how signaling networks make decisions, the dynamic interactions of proteins in the signal-transduction cascades are important rather than just creating static maps of pathways. Based on reaction kinetics, we have developed mathematical models to predict and analyze the impacts of the feedback loops in JNK cascades and the crosstalks between JNK and P38 kinase cascades. Feedback loops in JNK cascades and crosstalks between JNK and P38 kinase cascades plays the complementary roles in making the impacts on the activation of JNK and P38 kinases. JNK and P38 kinase cascades with feedbacks and crosstalks is a robust system.