Rubuta ci gaba don wannan sakin layi - Valdez ya wakilci Paraguay a gasar cin kofin duniya ta 2006 da 2010 na FIFA, ya kuma halarci gasar cin kofin duniya ta 2004
, 2011 da 2015 Copa América gasa; a cikin 2011 Paraguay ya gama a matsayin na biyu. Valdez ya buga wasanni sama da 70 a tawagar kasa kuma ya ci kwallaye 13, tare da daya daga cikin kwallaye nasa da ya zo a cikin nasara ta tarihi 1<unk>0 a kan abokan hamayyar Argentina a ranar 9 ga Satumba 2009 wanda ya tabbatar da cancantar Paraguay zuwa gasar cin kofin duniya ta 2010 kuma sakamakon shine nasarar Paraguay ta biyu a kan Argentina.