How to simultaneously execute two tasks?

Thanks for the replies. But from what I can understand, Using millis() for timing. A beginners guide - Using Arduino / Introductory Tutorials - Arduino Forum and the BlinkWithoutDelay IDE example only take care of scheduling the tasks, which is something I've done using the instruction
if (presentTime - previousTime_Red >= eventTime_Red)
my problem is not how to schedule tasks without using delay, it's how to execute two tasks at once.

UKHeliBob, I tried using 'if' instead of 'while' and it appears to instruct both LEDs to turn on (from what I see on the serial monitor) however, in reality, I can't see either of the LEDs turn on, ever.