The author proves the uniform boundedness and the ultimate uniform boundedness of the solutions of the system of functional differential equations \(x'= f(t,x_ t)\), where \(x_ t(s)= x(t+ s)\), \(-h\leq s\leq 0\), \(f: \mathbb{R}_ +\times C\to \mathbb{R}^ n\), \(C\) is the space of continuous functions \(\varphi: [-h,0]\to \mathbb{R}^ n\).