Koornwinder’s generalized Laguerre polynomials { L n α , N ( x ) } n = 0 ∞ \left \{ {L_n^{\alpha ,N}(x)} \right \}_{n = 0}^\infty are orthogonal on the interval [ 0 , ∞ ) [0,\infty ) with respect to the weight function 1 Γ ( α + 1 ) x α e − x + N δ ( x ) , α > − 1 , N ≥ 0 \frac {1}{{\Gamma (\alpha + 1)}}{x^\alpha }{e^{ - x}} + N\delta (x),\alpha > - 1,N \geq 0 . We show that these polynomials for N > 0 N > 0 satisfy a unique differential equation of the form \[ N ∑ i = 0 ∞ a i ( x ) y ( i ) ( x ) + x y ( x ) + ( α + 1 − x ) y ′ ( x ) + n y ( x ) = 0 , N\sum \limits _{i = 0}^\infty {{a_i}(x){y^{(i)}}(x) + xy(x) + (\alpha + 1 - x)y’(x) + ny(x)} = 0, \] where { a i ( x ) } i = 0 ∞ \left \{ {{a_i}(x)} \right \}_{i = 0}^\infty are continuous functions on the real line and { a i ( x ) } i = 1 ∞ \left \{ {{a_i}(x)} \right \}_{i = 1}^\infty are independent of the degree n n . If N > 0 N > 0 , only in the case of nonnegative integer values of α \alpha this differential equation is of finite order.