We studied the Fermi surface properties of YbCu2Si2 and YbCu2Ge2 with the tetragonal structure by measuring the de Haas-van Alphen (dHvA) oscillations, together with the energy band calculations. It was clarified that 4f electrons contribute to the Fermi surface of a valence fluctuating compound YbCu2Si2, but not to that of a divalent compound YbCu2Ge2. Namely, the Fermi surface of YbCu2Si2 contains the 4f-components considerably and the corresponding cyclotron effective mass m(c)* of the main Fermi surface is large, m(c)*=30-40m(0) (m(0) : rest mass of an electron). We also studied the heavy fermion properties of YbT2Zn20 (T : Co, Rh, Ir) with the cubic caged structure. The metamagnetic behavior or an abrupt nonlinear increase of magnetization was observed at 6 kOe in YbCo2Zn20, 63 kOe in YbRh2Zn20, and 97 kOe in YbIr2Zn20 for H parallel to < 100 >, which was measured at 60 mK in YbCo2Zn20 and 1.3 K in YbRh2Zn20 and YbIr2Zn20. The metamagnetic field is found to be a good parameter to reach the quantum critical point under pressure for YbIr2Zn20. By measuring the electrical resistivity under pressure and magnetic field, we clarified that the electronic state close to the quantum critical point is realized in YbIr2Zn20 at 5.2 GPa and also YbCo2Zn20 at ambient pressure. The corresponding heavy cyclotron effective mass of 100-500m(0) at 0 kOe was estimated from the field dependence of the root A value in the low-temperature electrical resistivity rho = rho(0) + AT(2) under pressure and magnetic field and the cyclotron mass obtained from the dHvA experiment at ambient pressure and high magnetic fields.