  The Sobolev-Laguerre polynomials form an orthogonal polynomial system with
respect to a Sobolev-type inner product associated with the Laguerre measure on
the positive half-axis and two point masses $M,N > 0$ at the origin involving
functions and derivatives. These polynomials have attracted much interest over
the last two decades, since they became known to satisfy, for any value of the
Laguerre parameter $\alpha\in\mathbb{N}_{0}$, a spectral differential equation
of finite order $4\alpha+10$. In this paper we establish a new explicit
representation of the corresponding differential operator which consists of a
number of elementary components depending on $\alpha,M,N$. Their interaction
reveals a rich structure both being useful for applications and as a model for
further investigations in the field. In particular, the Sobolev-Laguerre
differential operator is shown to be symmetric with respect to the inner
product.
