Complex patterns of intersection of linear with power-function curvilinear data point arrays are observed on ratio-ratio correlation plots of trace elements in the Alaer Palaeozoic granite pluton, Altay Mts., Xinjiang, northwestern China. Data points in the linear array are relatively lower in SiO 2 content and differentiation index (D.I.), and they become progressively decreased rightwards along the array in abundances of Zr and Hf, which could be better explained by mixing between zircon-rich restite and the granite melt. Data points in curvilinear arrays are higher in SiO 2 content and D.I. value and, therefore, have presumably suffered more extensive fractional crystallization. The complex patterns cannot be resolved with the classical models. Two models for the complex trace-element effects of mixing-fractional crystallization are developed in the paper, with which the patterns can be resolved. In all models, we begin with a linear data-array formed by simple two-component mixing, and then superpose fractional crystallization trends to generate a family of curves. Model (1) ( D 1 ≤ D 3, D 2 ≤ D 3 or D 1 ≥ D 3, D 2 ≥ D 3): in the general situation, fractional crystallization curves assume a cluster of concave-up or convex-up power-function curves which intersect the initial mixing line sloping positively. Special cases 1–3 ( D 1 = D 2 ≠ D 3 or D 1 ≠ D 2 = D 3 or D 2 ≠ D 1 = D 3): the fractional crystallization curve is transformed into a straight line. Special case 4 ( D 1 = D 2 = D 3): the fractional crystallization line coincides with the initial mixing line. Model (2) ( D 1 > D 3 > D 2 or D 1 < D 3 < D 2): fractional crystallization curves assume the form of hyperbolic curves which intersect the initial mixing line sloping negatively. In all of the two models the iso-fraction lines are uniformly steeper ( D 1 < D 2) or more gentle ( D 1 > D 2) than the initial mixing line. Iso-fraction lines increase ( D 1 < D 2) or decrease ( D 1 > D 2) progressively in slope with the decrease of residual liquid mass fraction F. Through modelling of the data point arrays on ratio-ratio correlation plots of trace elements, one can discern and distinguish between simple mixing, pure fractional crystallization and mixing-fractional crystallization composite processes. Initial compositions of the magma and the mixing modes can also be constrained. Through modelling the functional form, concavity or convexity, and the power index of the fractional crystallization curves, the relative incompatibility of trace elements can be estimated semi-quantitatively and the incompatibility sequence can be established. It is demonstrated through modelling that the Alaer granite pluton experienced mixing-fractional crystallization composite processes. The mixing mode is probably described by the restite model. The incompatibility sequence of the 7 concerned trace elements is D Th < D La < D Y ≈ D Nb ≈ D Ta < D Hf < D Zr. This incompatibility sequence may be applicable to the anatectic granites.