CuTCNQ (TCNQ = 7,7,8,8-Tetracyanoquinodimethane) is material which exhibits electrical resistive switching at 300K and has two structural forms (I and II), each with very different electrical and magnetic properties. We have used muon spin rotation/relaxation measurements to study the magnetic phase transition in CuTCNQ-II below 10K and we have evidence to suggest that the material is a 3D Heisenberg ferromagnet or antiferromagnet, but with an ordering temperature of about 10.8K. We propose to complete our study of this magnetic transition, which will include the dynamical behaviour of the magnetism in the vicinity of the ordering temperature, and also investigate the possibility of muon motion in CuTCNQ-I at high temperatures. We also propose to study the muon spin relaxation in CuTCNQ-I in order to obtain insight into the two muon implantation sites we have observed in CuTCNQ-I.