conditions for the not necessarily Hamiltonian system (in the paper we describe all these conditions). An important subclass of maximal dissipative (accumulative) separated conditions are those defined by a self-adjoint condition at the regular endpoint $a$ and the maximal dissipative (accumulative) boundary condition at the singular endpoint $b$. This subclass of boundary conditions may be useful in the theory of not orthogonal spectral functions associated with the system (we are going to touch upon this subject elsewhere).

Preliminaries
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Linear relations
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The following notations will be used throughout the paper: $\gH$, $\cH$ denote Hilbert spaces; $[\cH_1,\cH_2]$ is the set of all bounded linear operators defined on $\cH_1$ with values in $\cH_2$; $[\cH]:=[\cH,\cH]$; $A\up \cL$ is the restriction of an operator $A$ onto the linear manifold $\cL$; $P_\cL$ is the orthogonal projector in $\gH$ onto the subspace $\cL\subset\gH$; $\bC_+\,(\bC_-)$ is the upper (lower) half-plain of the complex plain.

Recall that a linear relation $T$ from a linear space $L_0 $ to a linear space $L_1$ is a linear manifold in the Cartesian product $L_0\times L_1$. It is convenient to write $T: L_0\to L_1$ and interpret $T$ as a multi-valued linear mapping from $L_0$ into $L_1$. If $L_0=L_1=:L$ one speaks of 