In this paper, we consider a non-self-adjoint ordinary differential operator defined on a finite interval by an nth-order linear differential expression with a nonzero coefficient at the \((n-1)\) th derivative and with two-point Birkhoff regular boundary conditions. We study the uniform equiconvergence of expansions of a given function in a biorthogonal series in eigenfunctions and associated functions (or, briefly, root functions) of this operator and expansions in an ordinary trigonometric Fourier series, as well as an estimate of the difference of the corresponding partial sums (or, briefly, the rate of equiconvergence) under the most general conditions on the expanded function and the coefficient at the \((n-1)\) th derivative. We obtain estimates for the difference of the expansions in terms of general (integral) moduli of continuity of the expanded function and the coefficient at the \((n-1)\) th derivative uniform inside the fundamental interval. From these estimates, we derive corresponding estimates in the case where moduli of continuity are bounded from above by slowly varying functions and, in particular, by logarithmic functions. Based on this, we formulate sufficient conditions for equiconvergence in the indicated cases. We prove these results using the author’s previously obtained estimate for the difference between the partial sums of expansions of a given function in a biorthogonal series in eigenfunctions and associated functions of the differential operator under consideration and expansions in a modified trigonometric Fourier series, as well as analogues of the Steinhaus theorem. The modification of the trigonometric Fourier series consisted in applying a very specific bounded operator to the ordinary trigonometric Fourier series expressed through the coefficient at the \((n-1)\) th derivative and its inverse operator to the expanded function.
