Magnetic, specific heat and transport studies on the solid solution LaCo13-x-Si-x (X = 3.8, 3.9, 4.0, 4.1, and 4.5) imply the existence of a critical composition x(crit) = 4 for the onset of magnetism. For alloys on the Co-rich side (x < 4) magnetic susceptibility measurements reveal weak ferromagnetism with a decrease of T-C with increasing x. These magnetic phase transitions are also seen in the electrical resistivity and specific heat measurements. At the stoichiometric composition with x = 4, namely for LaCo9S4, we observe full structural order within the space group I4/mcm, but magnetic order appears to be absent. LaCo9Si4 shows spin fluctuation behavior, which persists on the silicon-rich side x > 4. Resistivity, susceptibility and specific heat measurements on LaCo9Si4 provide strong indication for the presence of spin fluctuations with a T-2 temperature dependence of the electrical resistivity, an enhanced low temperature Pauli susceptibility chi(0)(LT) congruent to 47 x 10(-3) emu/mol at 2K and a large Sommerfeld value gamma = 200 mJ/(mol K-2). (C) 2003 Elsevier B.V. All rights reserved.