Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on $$\Bbb R$$, and we derive algebraic and differential relations for these MVOPs. A particular case of importance is that of MVOPs with respect to a matrix weight of the form W(x)=e$$^{-v(x)}$$e$$^{xA}$$e$$^{xA*}$$ on the real line, where v is a scalar polynomial of even degree with positive leading coefficient and A is a constant matrix.