Abstract: We considered the approximate controllability of the initial boundary value problems of a class of double coupled linear degenerate parabolic equations. We overcame the difficulty of the degeneracy of the equations,  constructed the control function by means of their conjugate problems, and proved the  approximate controllability of the initial boundary value problem  in L². In other words, for any initial value function and desired function  in L², we could  find a control function in L², which made the solution of the initial boundary value problem of the equation approximately reach the desired function in L² at the terminal time.

Key words: double coupled, degenerate parabolic equations, approximate controllability