  The standard block orthogonal (SBO) polynomials $P_{i;n}(x), 0\le i\le n$ are
real polynomials of degree $n$ which are orthogonal with respect to a first
Euclidean scalar product to polynomials of degree less than $i$. In addition,
they are mutually orthogonal with respect to a second Euclidean scalar product.
Applying the general results obtained in a previous paper, we determine and
investigate these polynomials when the first scalar product corresponds to
Hermite (resp. Laguerre) polynomials. These new sets of polynomials, we call
Hermite (resp. Laguerre) SBO polynomials, provide a basis of functional spaces
well-suited for some applications requiring to take into account special linear
constraints which can be recast into an Euclidean orthogonality relation.
