We have investigated evolution of transport and low-energy spin fluctuation properties of heavy Fermi liquid compounds YbAuCu4 and YbPdCu4 with the application of magnetic field. YbAuCu4 is found to be driven from the originally antiferromagnetically (AFM) ordered ground state (T-N similar to 0.8K) to a nonmagnetic Fermi liquid (FL) one through the field-tuned quantum critical point (QCP) at H-cr similar or equal to 13 kOe (T-N -> 0). In the vicinity of H-cr, the electrical resistivity measurement provides evidence for the increase in the inelastic scattering of heavy electrons, and the Cu-63 Spin-lattice relaxation rate measurement exhibits the occurrence of AFM spin order instability. Whilst, YbPdCu4 transforms from the originally ferromagnetically (FM) ordered ground state (T-C similar to 0.6K) into the nonmagnetic FL state, without any intermediate NFL phenomena. This result indicates that the competition of the field-stabilized FM correlation and field-destabilized AFM correlation plays an important role on the field-driven quantum critical phenomena. (C) 2007 Elsevier B.V. All rights reserved.