  Let $\Pi$ be a polar space of rank $n\ge 3$. Denote by ${\mathcal
G}_{k}(\Pi)$ the polar Grassmannian formed by singular subspaces of $\Pi$ whose
projective dimension is equal to $k$. Suppose that $k$ is an integer not
greater than $n-2$ and consider the relation ${\mathfrak R}_{i,j}$, $0\le i\le
j\le k+1$ formed by all pairs $(X,Y)\in {\mathcal G}_{k}(\Pi)\times {\mathcal
G}_{k}(\Pi)$ such that $\dim_{p}(X^{\perp}\cap Y)=k-i$ and $\dim_{p} (X\cap
Y)=k-j$ ($X^{\perp}$ consists of all points of $\Pi$ collinear to every point
of $X$). We show that every bijective transformation of ${\mathcal G}_{k}(\Pi)$
preserving ${\mathfrak R}_{1,1}$ is induced by an automorphism of $\Pi$ and the
same holds for the relation ${\mathfrak R}_{0,t}$ if $n\ge 2t\ge 4$ and
$k=n-t-1$. In the case when $\Pi$ is a finite classical polar space, we
establish that the valencies of ${\mathfrak R}_{i,j}$ and ${\mathfrak
R}_{i',j'}$ are distinct if $(i,j)\ne (i',j')$.
