Its common practice in narrow band and broad band circuits to bypass with a range of capacitors to match the range of frequencies that the circuit uses and the range of frequencies the circuit might misbehave with (ie be unstable at) if it wasn't bypassed properly. This latter range is typically much bigger than many people think and depends on the type of semiconductors used. You might be building an amplifier to work at 60 MHz but only use a 0.01 uF ceramic bypass cap, which would be a mistake because the amplifier might have a lot of gain at 2 Mhz and suffer parasitic oscillation because the power supply is poorly bypassed at that frequency.
All digital logic circuits are broadband circuits with bands of interest from DC to, let's say, ten times the highest clock frequency (rough rule of thumb). So it is best if you can bypass an 80 MHz processor up to 800 MHz or so. This requires a ceramic capacitor of small value, and preferably surface mounted to avoid lead inductance (you don't need a high Q type cap for this, just a regular one is fine). The effective range of a tantalum cap depends on the value and voltage rating, but let's just talk rules of thumb. Here's mine. I would not use an aluminum electrolytic as bypass above 50 Khz, nor a tantalum cap above 2 MHz. I would use ceramic above 2 Mhz. I would use a 0.1 or 0.01 uF ceramic for logic circuits capable of up to 30 MHz toggle rates, (in other words with significant energy up to 300 MHz) and I would add a separate small value cap, say 33 pF for example, to cover toggle rates up to 100MHz (ie. energy up to 1 GHz). The cap that is intended for the highest frequency bypassing must be placed the closest to the supply pin and ground pin of the IC you are bypassing. So the smallest value gets the place of honour, followed by the larger value ceramic cap. The tantalum can be anywhere nearby and the aluminum electrolytic just needs to be on the same pcb somewhere.
Have a look at some good radio schematics. Critical sections, like frequency synthesizer chip for example, are bypassed with two or three ceramic caps in parallel, usually a large value, and a small value, and sometimes a medium value too.
So, for your 80 Mhz processor, you are poorly bypassed using only a 10 uF tantalum and should add at least a 0.1 uF ceramic and preferably one of those plus one 100 pF cap (although this is perhaps too conservative for most hobbyists).