The compound SrCo2As2 with the body-centered tetragonal ThCr2Si2 structure is known to remain paramagnetic down to a temperature T=0.05 K, but inelastic neutron scattering studies have shown that both ferromagnetic (FM) and antiferromagnetic (AFM) fluctuations occur in single crystals. Thus it is of interest to study how the magnetism evolves on doping SrCo2As2. Previous work on polycrystalline samples of Sr(Co1−xNix)2As2 indicated the development of AFM order for 0Ab initioelectronic-structure calculations for x=0 and 0.15 indicate that a flat band with a peak in the density of states just above the Fermi energy is responsible for this initial magnetic-ordering behavior on Ni doping. The AFM ordering is observed in the range 0.013≤x≤0.25 with the ordered moments aligned in the ab plane and with a maximum ordering temperature TN=26.5 K at x=0.10. The Curie-Weiss-like T dependence of χ in the paramagnetic (PM) state indicates dominant FM interactions. The behavior of the anisotropic susceptibilities below TN suggests a planar helical magnetic ground state with a composition-dependent pitch based on a local-moment molecular-field-theory model, with FM interactions in the ab plane and weaker AFM interactions along the helix c axis. However, the small ordered (saturation) moments ∼0.1μB per transition metal atom, where μB is the Bohr magneton, and the values of the Rhodes-Wohlfarth ratio indicate that the magnetism is itinerant. The high-field M(H) isotherms and the low-field χ−1(T>TN) data were successfully analyzed within the framework of Takahashi's theory of FM spin fluctuations. The Cp(T) at low T exhibits Fermi-liquid behavior for 0≤x≤0.15, whereas an evolution to a logarithmic non-Fermi-liquid (NFL) behavior is found for x=0.2 to 0.3. The logarithmic dependence is suppressed in an applied magnetic field. The low-Tρ(H=0,T) data show a T2 dependence for 0≤x≤0.20 and a power-law dependence ρ(H=0,T)=ρ0+ATn with ndependence, suggesting both doping- and magnetic-field-tuned quantum critical phenomena. These low-T NFL types of behavior observed in the Cp and ρ measurements are most evident near the quantum critical concentration x≈0.3 at which a T=0 composition-induced transition from the AFM phase to the PM phase occurs.