We present several novel methods for solving general (pseudo-) monotone variational inequalities. The first method uses fixed stepsize and is similar to the proximal reflected gradient method: it also requires only one value of operator and one prox-operator per iteration. However, its extension — the dynamic version — has a notable distinction. In every iteration it defines a stepsize, based on a local information about operator, without running any linesearch procedure. Thus, the iteration costs of this method is almost the same as in the first one with a fixed stepsize, but it converges without the Lipschitz assumption on the operator. We further discuss possible generalizations of the methods, in particular for solving large-scale nonlinear saddle point problems. Some numerical experiments are reported.