We present nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements performed on single crystalline Ce2CoAl7Ge4, a member of a recently discovered family of heavy fermion materials Ce2M Al7Ge4 (M = Co, Ir, Ni, or Pd). Previous measurements indicated a strong Kondo interaction as well as magnetic order below TM = 1.8 K. Our NMR spectral measurements show that the Knight shift K is proportional to the bulk magnetic susceptibility χ at high temperatures. A clear Knight shift anomaly (K ∝ χ) is observed at coherence temperatures T * ∼ 17.5 K for H0 ĉ and 10 K for H0 â at the 59 Co site, and T * ∼ 12.5 K at the 27 Al(3) site for H0 â characteristic of the heavy fermion nature of this compound. At high temperatures the 59 Co NMR spin-lattice relaxation rate T −1 1 is dominated by spin fluctuations of the 4f local moments with a weak metallic background. The spin fluctuations probed by 59 Co NMR are anisotropic and larger in the basal plane than in the c direction. Furthermore, we find (T1T K) −1 ∝ T −1/2 at the 59 Co site as expected for a Kondo system for T > T * and T > TK . 59 Co NQR T −1 1 measurements at low temperatures indicate slowing down of spin fluctuations above the magnetic ordering temperature TM ∼ 1.8 K. A weak ferromagnetic character of fluctuations around q = 0 is evidenced by an increase of χT versus T above the magnetic ordering temperature. We also find good agreement between the observed and calculated electric field gradients at all observed sites. 1 driven by local moment spin fluctuations agree well with the experimentally observed value. We also find that (T 1 T K) −1 ∝ T −1/2 at the 59 Co site as expected for a Kondo system at high temperatures relative to T * and T K [15]. At low temperatures, 59 Co arXiv:1812.08633v1 [cond-mat.str-el]