A hybrid method or apparatus for processing OpenGL display list commands. A deamon intercepts display list commands issued by a client to an OpenGL stack. Responsive to a newList [list commands] endList sequence: the daemon stores a representation of a first subset of the list commands; and creates, in the stack, a display list corresponding to a second subset of the list commands. Responsive to a callList command: the daemon issues to the stack at least one immediate mode command corresponding to the first subset of the list commands and at least one callList command invoking the display list corresponding to the second subset of the list commands. The daemon may also store a representation of an expression or function. Responsive to the callList command, the daemon may evaluate the expression or function and conditionally change the step of invoking the display list based on the outcome.