Creo + infinitive
 

Here's the example from the book I'm reading:

Se comporta con cautela; creo saber la razón.

This sounds strange to me and I don't think I've ever come across this construction before (but then again, my memory has failed me before). My inclination would be to say:

Se comporta con cautela; creo que yo sé la razón.

Can creo saber la razón be used in the sense of I think I know the reason.

That is the correct way to I think I know the reason. Do not use pensar here. If the subject doesn't change, there is no need for the secondary clause. Just use the infinitive.

Thanks amigo.

yes, you can use it like this I think so: eso creo or I don´t think so: no lo cre
I don´t think in her all the time.*_*:.-.-.--.-.-.-.-.-.-.-.-.-.-´+,

This sentence should be 'I don't think about her all the time' and it uses the verbal phrase pensar en in Spanish:
No pienso en ella todo el tiempo.

The other verb creer en, as in 'No creo en ella,' would be translated 'I don't believe in it (something feminine).'

oh, yes, you´re right, sorry, I didn´t realize.*_* thank you.

Creo saber la razón and creo que sé la razón are both correct and interchangeable.

Se comporta con cautela; (yo) creo saber la razón.
He/She behaves cautiously, I think I know the reason.

As David sayed, the construction it's OK. The use of "creo" means that I have other data/references which make me "believe" I know the reason.
Your other option "creo que yo sé la razón" it's also correct, but as spaniards, we try to say it shorter :D
Other examples
"creo sentir algo profundo"/"creo que yo siento algo profundo"
"pienso sanar pronto"/"pienso que yo sanaré pronto"
"imagino vivir de otra manera"/ "imagino que yo puedo vivir de otra manera"
Saludos :D

It can be said in both ways meaning the same. Perfect Castelian.

What's more, in "... creo que yo sé la razón."

You can take the "Yo" too. hehehe :-)

But it's true. Perfect Castelian.

Hernan.

Gracias a todos por la ayuda.