Hi Steven ,

I think you are confusing the futur antérieur (future perfect) and the conditionnel antérieur (past conditional).

J'aurais dû = I should have
j'aurais pu = I could have

Note: aurais has an 's' here.

The futur antérieur relates to an action which is prior to another in the futur simple:

Dans deux ans ils auront fini les travaux, ( In 2 years time they will have finished the works)

Quand nous aurons fini les travaux dans la maison, nous irons en vacances. (When the work in the house is finished, we'll go on holiday)

Dés que nous aurons arrêté de fumer, nous repeindrons la maison.( Once we have stopped smoking we'll repaint the house)

Note that after words like when, as soon as, once denoting time we use the future in French as opposed to the present in English.

Hope this helps!

Just to add a bit extra to Cécile's great answer, the first person forms of these two tenses sound identical, so you can only tell which is meant from the context. The conditional past introduces modal verbs (would/should) and so does devoir and that can get very complicated and confusing quickly.

Let's make it easier with a simpler verb (say 'manger') first:

Quand j'aurai mangé je t'appellerais. (Future perfect: When I will have eaten I'll call you. Or in more idiomatic English, Once I have eaten I'll call you.)

Si j'avais eu faim j'aurais mangé. (Conditional past: If I'd been hungry I would have eaten.)

In most cases, there's another tense and clause involved that gives clear context and often the literal translation isn't even in the same tense as the same idiomatic expression in English.

DEVOIR:

It's incredibly hard to contrive an example with devoir for the future anterieur (in either language) - it's unlikely you'll come across it at all.

J'aurai dû faire ça avant ton retour. (Future perfect: I will have had to do that by the time you get home.)

J'aurais dû t'appeler mais j'ai oublié. (Conditional past: I should have called you but I forgot.)

Hope that helps to clear away some of the confusion!

P.S. You can look up how to conjugate avoir to see (and listen to) all six forms of the [kwiziq_link type="lexical_feature" id=57] and [kwiziq_link type="lexical_feature" id=48].