Rolemaster Companion IV introduced the Action Point Based Turn Sequence system that could be used to replace "round system". It was interesting, but too complicated and still included "rounds".
What we did in our group was to adapt the action points and got rid of rounds.
Every action spends some action points, the exact amount depending on task and character's quickness, skill level, health and so on. There's no "turns" or "rounds", just a cumulative Action Point (AP) rolling until tactical situation is over. Actions follow each other seamlessly. 40 Action Points equals to 10 seconds or one "round" if that information is necessary.
Classical example: This may seem incredibly complicated, but I think that normal Action% system with the same example, stating percentages in explaining manner would suffer equally.
Jack and Jones are walking on the road, and encounter some orcs. Distance is 100 feet. GM rolls for some Alertness rolls for everyone, and describes to players some first-look things from orcs (like weaponry, armors, size etc) depending on the success level. GM states that tactical battle begins, rolls laminated hex map on table, draws some trees and stuff on it and throws in miniatures.
GM calls for Orientation rolls for everyone. This roll is a catch-all initiative roll, perhaps misleadingly named but anyway. [Orientation roll is modified by QU/SD bonus average + 50 + d100 + gm mods, result is checked from the short table, giving usually something around 5 - 30 AP). Orientation AP (Action Point) says the amount of action points that goes by before the character can do anything. 5AP is quite a norm for experienced characters, having Instinctive Maneuver ranks, Lightning Reaction talents and so on.
After Orientation rolls, we know exactly who goes first (in tie, it's either same time action or the one with greater QU bonus, stat etc goes first).
GM asks for intentions, players state theirs and GM writes down orcs intentions and the moment when actions are resolved. For example, orc 1 draws a sword from scabbard which takes ½ of normal attack Action Points (without quickdraw action) - let's say it's 18AP action. Since orc 1's Orientation was 10AP's from start, the sword is at hand on 10+18=28AP.
Orc 2 rolled 5AP for his Orientation and decides to shoot with short bow at Jack. Loading a bow takes 24AP's + shooting 10AP's more, so GM marks AP 5 + 24 + 10 = 39 as a action resolution phase for orc 2.
Orc 3 decides to run behind the nearest tree so that he can check the situation from someplace safe. Orientation roll states AP15, nearest tree being some 20feet away. GM calculates that orc runs (120feet/rnd) the 20 feet in (20feet/120)*40 = 7AP's. He's behind the tree at AP 15+7=AP22.
Orc 4 fumbles his Orientation roll, so he's totally surprised and can do nothing in next 40AP's.
Jack's player states that his Orientation resulted in AP5, and his intention is to draw a sword with quickdraw. Since none is doing anything at AP 5, he rolls for his Quickdraw skill, a success, which means 1/4 of attack time = 8AP's. His new intentions are called at AP 5+8=AP13.
Jones rolls for AP 10, and states that he's casting a class I directed spell, taking 10AP's. He targets the orc with a bow who he now sees is probably loading his bow. GM secretly rolls for orc's alertness if they could have any change to notice what's going on. Rolls fail so no actions because of spell casting.
Everyone takes care of his own numbers, which is basically just a next action resolution phase. Jack's paper says AP 13 and Jones's paper says AP 20.
And from that it all really starts:
At AP 13 Jack is ready for further action. GM says that one orc is loading his bow and Jones is apparently casting a spell (assuming it's apparent from casting style, let's say it is an essence spell). This information is available, since the actions have already started (orc started it on AP 10 as well as Jones). Jack's player curses and decides to run behind a tree, shouting a warning to Jones. Distance to nearest tree is 30 feet and Jack's running speed is 150feet/rnd, so it takes (30/150)*40=8AP's. So Jack's next Action Phase is 13 + 8 = AP 21. He runs and shouts to Jones at the same time: "Run for cover". GM says its such a small message that it really happens at the same time. Had Jack decided to speak longer, he would continue speaking while at cover. GM rolls for Jones's routine Alertness and he gets the message but decides to pay no attention while casting a spell.
Meanwhile, Orc 1 sees that one human draws a sword and runs behind the tree while he self is drawing his sword. The orc is slightly worried since the human draw a sword incredibly fast.
Orc 2 is loading his bow and sees that his intended target ran for cover. Since the load phase is still going on (probably setting a arrow to string now), he just decides to shoot Jones instead, taking no penalty since the actual shooting phase has not yet started. Orc still intents to shoot at AP 39.
GM calls for actions. Jones says he's ready at 20, so he's next. Jones's been casting a shock bolt spell and now's the resolution phase. Spell casting is a success and after damage resolution, orc has suffered some damage and is at stunned state. Jones feels a momentary stress of spell casting and knows he's not able to cast another spell yet (spell casting interval = spell level/2 + 20AP's). Jones states he intents to run for cover as Jack did. He's at cover at AP 20 + 9 = 29.
Orc 2: While loading, he sees a flash at Jones's hand...(AP 20)...and feels the heat of shock bolt and intense pain on his side. Orc is stunned and cannot continue his action of loading the bow for next 40 AP's (one old-time "round" of stun). In short, orc is stunned until AP 20+40=60. Among other things, stun results in need of another and immediate orientation roll, and now with some penalties. GM rolls orc's new AP to be 20, so orc's next action phase is 20(stun result)+20 (new orientation).
Orc 3 is ready for action and behind the tree at AP 23. He scans the area shortly (10AP's of Observation), so his next Action Phase is at AP 33. During this scan (23-33) he sees how Jack has disappeared and Jones is running for cover. He also sees that one of his comrades has been hit by some nasty thing, one is standing still like an moron and one is drawing his clumsy sword from his back and is finally ready for an action.
After a scan (at AP 33) Orc 3 shouts to moron (orc 4) to follow him, using his Leadership skill (GM rolls success). Orc 4 instantly runs behind the same tree as orc 3.
What I'm trying to show, is that round system is an abstraction that is not at all necessary. Actions can follow each other and synchronize, creating a intriguing tactical situation, a game of it's own especially if using hex. Any action possible can be simulated this way, with varying intervals and individual AP's. Everyone follows his own next Action Phase and alerts when time is right.
Many things in RM refer to 10sec rounds, like stuns, spells etc. This is easily solved as 1 rnd = 40AP's.
What is needed in this system is a Action Point table which lists a base AP cost of any action. RM Companion IV page 16 is quite full of these.
We've been playing with this system for some 10 years now, and it's fluent.
In short, you only need to know how long your action takes AP's and roll.