[рони]

sergey24,
c "translate.owl.carousel" можно так

$(function() {
    $(".owl-carousel").owlCarousel({  loop: true,
        startPosition: -1,
        items: 3,
        nav: true,
        navText: ['<img src="/left.png" alt="" />', '<img src="/right.png" alt="" />'],
        dots: false
    }).on({"translated.owl.carousel": setCls, "translate.owl.carousel" : remCls});

    function setCls() {
        $(".owl-item").filter(".active").eq(1).addClass("red")
    }
    function remCls() {
        $(".owl-item").removeClass("red")
    }
    setCls()
});