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LnBaCo2O5.5 (Ln=Gd, Eu) and Sr3Ru2O7 are examples of weakly magnetic systems of 3d and 4d transition metal oxides, respectively. The former is nonmetallic and exhibits magnetic properties of two sublattice magnetic systems with an in-plane ferromagnetic interaction and a relatively weak temperature dependent inter-plane magnetic coupling. The latter is a paramagnetic metal with strongly correlated electrons near a magnetic instability. The magnetization, resistivity and magnetoresistance (MR) of single crystals of GdBaCo2O5.5 and EuBaCo2O5.5 are measured over a wide range of dc magnetic fields (up to 30 T) and temperature. We confirm that GdBaCo2O5.5 and EuBaCo2O5.5 have a metal-insulator transition accompanied by a spin-state transition at TMI » 365 and 335 K, respectively. The data suggest an equal ratio of low spin (S=0) and intermediate spin (S=1) Co3+ ions below TMI, with no indication of additional spin state transitions. The low field magnetization shows a transition to a highly anisotropic ferromagnetic phase, followed by another magnetic transition to an antiferromagnetic phase at a slightly lower temperature. Significant anisotropy between the a-b plane and c axis was observed in magnetic and magnetotransport properties for both compounds. For GdBaCo2O5.5, the resistivity and MR data imply a strong correlation between the spin-order and charge carriers. For EuBaCo2O5.5, the magnetic phase diagram is very similar to its Gd counterpart, but the low-T MR with current flow in the ab plane is positive rather than negative as for GdBaCo2O5.5. The magnitude and the hysteresis of the MR for EuBaCo2O5.5 decrease with increasing temperature, and at higher T the MR changes sign and becomes negative. The difference in the behavior of both compounds may arise from a small valence admixture in the nonmagnetic Eu ions, i.e. a valence slightly less than 3+. The specific heat and electrical resistivity of Sr3Ru2O7 single crystals are measured in several magnetic fields applied along the c-axis for temperatures below 2 K and at fields up to 17 T. Near the critical metamagnetic field at B1*~7.8 T, the electronic specific heat divided by temperature increases logarithmically as the temperature decreases, over a large range of T, before saturating below a certain T* (which is sample dependent). This crossover from a non-Fermi Liquid to a Fermi Liquid state is also observed in the resistivity data near the critical metamagnetic field for I || c and B || c. At the lowest temperatures, a Schottky-like upturn with decreasing temperature is observed. The coefficient of the Schottky anomaly exhibits a field dependence similar to that of g, implying an influence by the electrons near the Fermi surface on the Schottky level splitting.