We have measured the muon-spin rt laxation (mu SR) in La0.6Sr0.4MnO3 and in its layered sister system La1.2Sr1.8Mn2O7 to study the influence of dimensionality on their magnetic properties. Both compounds show ferromagnetic ordering with decreasing temperature. Above their Curie temperatures we followed the spin fluctuations. While the electron spin fluctuations in the three-dimensional La0.6Sr0.4MnO3 slow down critically as the transition temperature is approached they remain finite in the layered material La1.2Sr1.8Mn2O7. We can fit them to 2D critical behaviour with a lower T-C. In addition, we observe a spin precession signal in the ferromagnetically ordered state in La1.2Sr1.8Mn2O7; the temperature dependence of the muon precession frequency is in agreement with a three-dimensional character of the ordering. (C) 2000 Published by Elsevier Science B.V. Ail rights reserved.