While his brother David conquered a number of Byzantine provinces in northwestern Anatolia, Alexios defended his capital Trebizond from an unsuccessful siege by the Seljuk Turks around the year 1205.
Mentres o seu irmán David conquistaba varias provincias bizantinas no noroeste de Anatolia, Aleixo defendeu a súa capital de Trebisonda dun infrutuoso asedio polos turcos selxúcidas ao redor do ano 1205.