A B757-200 flight crew encountered a variety of electrically based autoflight system anomalies.

Narrative

Shortly after takeoff; on climb out; the ASA switched to 'NO LAND 3'. No problem; we didn't plan to use a Cat 2/3 approach at our destination. We were cruising at 35000 ft; using the center autopilot. It was about 3.5 hours into the flight; when the Center autopilot kicked off; accompanied by the Master Warning & Caution Lights and Warning Horns. The Captain was the pilot flying and took control of the aircraft; while we attempted to assess the problem. There was the faint smell of electrical components overheating. We donned or oxygen masks and goggles; and established communications with each other; and then we started looking for the nearest available airports. We were approximately 100 miles north of the Venezuela/Brazil boarder. Bogotá was over 460 miles west and Manaus was over 680 miles south. We never saw any smoke; by pulling the oxygen mask off our face briefly we quickly realized the smell had dissipated. Only the right autopilot would engage at this time. We simultaneously lost: Center & Left Autopilot; Left and Center Flight Directors; Auto Throttles; and ASA went to 'NO AUTOLAND'. There were no EICAS messages; only forward panel lights and Master Warning and Caution Lights. On the Status page there was a WXR SYS. We established communications with the company to help with the decision to divert or continue. A decision was made to continue towards Manaus. Approximately 30 minutes after the initial incident we noticed the ASA went back to 'NO LAND 3'. We pushed the reset button on the ASA panel and fault was cleared. Now we realized the Auto throttles; Flight Directors; and Autopilots were operational again. We decided to continue flight with the Right Autopilot engaged since we had no confidence in the other two. Throughout the next four plus hours of flight the ASA; auto throttles and flight directors cycled from an operational state to failure several times. We did not attempt to check the left and center autopilots any further. Upon landing multiple write ups were put in the logbook and the mechanics and departing crew were briefed.