  We consider properties of semi-classical orthogonal polynomials with respect
to the generalised Airy weight
\[\omega(x;t,\lambda)=x^{\lambda}\exp\left(-\tfrac13x^3+tx\right),\qquad x\in
\mathbb{R}^+,\] with parameters $\lambda>-1$ and $t\in \mathbb{R}$. We also
investigate the zeros and recurrence coefficients of the polynomials. The
generalised sextic Freud weight
\[\omega(x;t,\lambda)=|x|^{2\lambda+1}\exp\left(-x^6+tx^2\right), \qquad x\in
\mathbb{R},\] arises from a symmetrisation of the generalised Airy weight and
we study analogous properties of the polynomials orthogonal with respect to
this weight.
