The trajectory tracking problem is considered for a general class of non-linear time-delay systems. The existence of causal static state feedback solutions is investigated within an algebraic approach. Two classes of causal static compensators are considered that either involve delayed dynamics or not. Sufficient conditions are derived which are weaker than the ones existing in the current literature. These results are innovative for both linear and non-linear time-delay systems. The most advanced results do not imply a maximal loss of observability in opposition to more standard solutions.