Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces We establish global well-posedness for both the defocusing and focusing complex-valued modified Korteweg–de Vries equations on the real line in modulation spaces Ms,2p (R), for all 1 p < 1 and 0 s < 3/2 − 1/p. We will also show that such solutions admit global-in-time bounds in these spaces and that equicontinuous sets of initial data lead to equicontinuous ensembles of orbits. Indeed, such information forms a crucial part of our well-posedness argument. 7 3 615-637 615-637 Mathematical Sciences Publishers