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Resonant Ultrasound Spectroscopy has been used to characterise strain coupling and relaxation behaviour associated with magnetic/magnetoelectric phase transitions in GdMnO3, TbMnO3 and TbMn0.98Fe0.02O3 through their influence on elastic/anelastic properties. Acoustic attenuation ahead of the paramagnetic ��� colinear-sinusoidal/incommensurate/antiferromagnetic transition at ~41 K correlates with anomalies in dielectric properties and is interpreted in terms of Debye-like freezing processes. A loss peak at ~150 K is related to a steep increase in electrical conductivity with a polaron mechanism. The activation energy, Ea, of ��� ~0.04 eV from a loss peak at ~80 K is consistent with the existence of a well-defined temperature interval in which the paramagnetic structure is stabilised by local, dynamic correlations of electric and magnetic polarisation that couple with strain and have relaxation times in the vicinity of ~10-6 s. Comparison with previously published data for Sm0.6Y0.4MnO3 confirms that this pattern may be typical for multiferroic orthorhombic RMnO3 perovskites (R = Gd, Tb, Dy). A frequency-dependent loss peak near 10 K observed for TbMnO3 and TbMn0.98Fe0.02O3, but not for GdMnO3, yielded Ea ��� ~0.002 eV and is interpreted as freezing of some magnetoelastic component of the cycloid structure. Small anomalies in elastic properties associated with the incommensurate and cycloidal magnetic transitions confirm results from thermal expansion data that the magnetic order parameters have weak but significant coupling with strain. Even at strain magnitudes of ~0.1-1 ���, polaron-like strain effects are clearly important in defining the development and evolution of magnetoelectric properties in these materials. Strains associated with the cubic - orthorhombic transition due to the combined Jahn-Teller/octahedral tilting transition in the vicinity of 1500 K are 2-3 orders of magnitude greater. It is inevitable that ferroelastic twin walls due to this transition would have significantly different magnetoelectric properties from homogeneous domains due to magnetoelastic coupling with steep strain gradients., This work was funded by EPSRC Grant No. EP/ P024904/1 (UK). RUS facilities were established through grants from the Natural Environment Research Council (Grants No. NE/B505738/1 and No. NE/F017081/1) and the Engineering and Physical Sciences Research Council (Grant No. EP/I036079/1) to MAC. The work at the University of Warwick was supported by EPSRC,UK through Grant EP/T005963/1.