 Miļevskis started playing under the best Latvian youth football coach Krišs Maisītājs in the Riga football school, later he played with FK Progress under Jānis Skredelis.In 1981 Miļevskis joined Daugava Rīga and with his smart and elegant playing style soon attracted the interest of both fans and specialists.He got invitations to play for several top Soviet clubs including FC Dynamo Kyiv, FC Dynamo Moscow and PFC CSKA Moscow but eventually he joined Spartak Moscow.