<p>We study the steerability dynamics of two types of Bell-like states in double Jaynes–Cummings model under noiseless and noisy environments. In the absence of noise, we derive analytical expressions for the maximal violations of the three-setting Cavalcanti, Jones, Wiseman, and Reid (CJWR) linear steering inequality for the evolved states, demonstrating that the sudden death phenomenon of steering occurs for both types of initial states. Specifically, we identify a steering invariant that remains invariant under temporal evolution, indicating a ‘transfer’ of steerability among subsystems over time. The influence of asymmetric coupling strengths between the two Jaynes–Cummings models on quantum steerability dynamics is also investigated. By analytically solving the Lindblad form of the master equation, we study the steerability dynamics of two-qubit states in a phase-damping noisy environment, providing a stability analysis for the two types of Bell-like states under noise.</p>