  Excited quark production at future $\gamma p$ colliders is studied. Namely,
$\gamma p \to q^{*}X$ with subsequent $q^{*}\to gq$ and $\gamma q $ decay
channels are considered. Signatures for discovery of the excited quark and
corresponding standard model backgrounds are discussed in detail. Discovery
limits for excited quark masses and achievable values of compositeness
parameters $f_s$, $f$ and $f^\prime $ are determined.
