The quasi 1-D magnets ANiCl3: A = Cs, Tl, order magnetically in two steps. A partially ordered state between TN1 and TN2 and a fully magnetic ordered state below TN2. RbNiCl3 has a crystallographic unit cell similar in size to TlNiCl3. The radius of the Tl+ ion is a little smaller than the radius of Rb+ ion. However, RbNiCl3 orders only with one TN at1 T = 0K. We have a studied the magnetic ordering in CsNiCl3 and KNiCl3 via muon spin relaxation behaviour.The complete the investigation of this series we propose to study the temperature dependence of the muon spin relaxation in TlNiCl3(TN1 =18.3K and TN2 = 12.5K). A similar study is proposed for RbNiCl3. The temperature dependence of the muon spin relaxation will show if there is only one magnetic transition temperature. EMU data from the test experiment show the presence of 2 stopping sites. We request 4 days beam time on EMU.