In this work, a system of singularly perturbed differential equations of the 4th order with a small parameter at the highest derivative and a turning point is considered. The turning point x=0 is located in the end of the segment [-l;0] under consideration. The coefficients of a given matrix are infinitely differentiable functions on a given interval. The goal is to construct a uniform solution asymptotics for a system of singularly perturbed differential equations with a differential turning point on the segment [-l;0]. In this case, the spectrum of the limit operator contains multiple and identically zero elements. The uniform asymptotic solution is constructed by the method of essential-singular functions using the Airy functions [0;l] and their derivatives. Studies have shown that the Apparatus of Airy functions and model equations is quite effective for constructing a uniform asymptotic solution of problems with turning points. It was also established that in order to select these functions along with the independent variable it is necessary to introduce a new variable t of the segment [0;l]. As a result, an extended problem will be obtained, which will make it possible to formally find the solution in the form of series with a small parameter. The constructions of the solutions are obtained by sequentially solving the systems of iterative equations, which at a certain step of the iterations make it possible to determine all the components of the sought-after vector functions with an accuracy of two scalar factors that form an arbitrary vector. The regularizing function Bi(t) is chosen in such a way that the function increases indefinitely when t approaches the infinity. The conducted studies showed that for any ratio of the signs of the matrix coefficient near which the inflection point is located, it is not possible to write down a smooth solution in the form of a single analytical expression. The solution of a degenerate vector equation in the general case has a discontinuity of the second kind at the inflection point, so it cannot be used explicitly to construct the asymptotic solution of this problem. For this purpose, a technique from the classical theory of linear differential equations was applied and solutions for a degenerate equation of the 2nd order were obtained.