In the design of coastal and offshore facilities, it is customary to estima
te parameters of a design sea state corresponding to a specified return per
iod or annual risk, and then develop an estimate of the expected largest in
dividual wave height within that sea state. It turns out that the expected
largest individual wave height in a sea state with a specified return perio
d may be significantly different than the maximum individual wave height wi
th the same return period. The present paper serves to highlight this diffe
rence. It describes for different situations the calculation of the long-te
rm distribution of individual wave heights and of the maximum individual wa
ve height with a specified return period. Results are presented (i) for a s
pecified wave scatter diagram; (ii) for hindcast wave parameters for a sequ
ence of storms or hurricanes; and (iii) for a range of parameters relating
to analytical descriptions of long-term sea states. In addition, a comparis
on of alternative methods of computation is made. It is found that the maxi
mum individual wave height with a given return period is generally apprecia
bly larger than the expected maximum individual wave height in a sea state
with the same return period.