Ramba uchiverenga ndima ino - Cocu akatanga kutamba nechikwata chenyika cheNetherlands muna 1996 uye akaonekwa paWorld Cup ya1998, achihwina zvibodzwa zviviri asi achirovha penareta mumasemi-fainari achipesana neBrazil. Akatambawo pa2006 World Cup, pamwe ne1996, 2000 uye 2004 European Championships
. Cocu akasvika kuma semi-fainari mumakwikwi maviri ekupedzisira uye muna 2004, akashanda semutungamiriri wechikwata cheDutch. Nemitambo 101, Cocu ari wechisere pane runyorwa rwevazhinji veDutch nyika dzese. Munguva yebasa rake, ainyanya kutamba semudziviriri "mutambi" pakati penhandare, asi akazozivikanwa zvakaenzana nekugona kwake kuiswa semudziviriri, kumashure, winger kana kumberi.