The first order ordinary differential equations \(y'(x) = p_0 (x)y(x) + \sum ^k_{i = 1} p_i (x)y (\psi_i (x))\) (with \(k\) deviating arguments, \(k \geq 1\) is fixed) are divided into equivalence classes by means of transformations \(x = h(t)\) and \(z(t) = f(t) y(h(t))\). The author deals with the classes that contains an equation with \(k\) constant deviations \(\psi_i (x) = x - c_i\). A criterion when two equations with constant deviations lie in the same class is established. This result is explicitly applied to the case \(p_0 \equiv 0\), \(k = 1\), \(p_1 = \text{const}\).