  The paper deals with the expected maxima of continuous Gaussian processes $X
= (X_t)_{t\ge 0}$ that are H\"older continuous in $L_2$-norm and/or satisfy the
opposite inequality for the $L_2$-norms of their increments. Examples of such
processes include the fractional Brownian motion and some of its "relatives"
(of which several examples are given in the paper). We establish upper and
lower bounds for $E \max_{0\le t\le 1}X_t$ and investigate the rate of
convergence to that quantity of its discrete approximation $E \max_{0\le i\le
n}X_{i/n}$. Some further properties of these two maxima are established in the
special case of the fractional Brownian motion.
