A method for reducing resonant vibrations and dynamic loads of cranes, whose vertical motion of the pay load is controlled by a boom winch controlling the luffing motion of a pivoting boom and a hoist winch controlling the vertical distance between a boom tip and the load, characterized by that the method includes the steps of: - determining resonance frequencies of the coupled crane boom and load system, either experimentally or theoretically at least from data on inertia of the boom and stiffness of at least a boom rope, a hoist rope, a pedestal and an A-frame; - automatic generation of a damping motion in at least one of said winches (24, 36), that counteract dynamic oscillations in the crane by means of either: feedback of high-pass- or band-pass-filtered values of measured tension forces in the boom rope and in the hoist rope by applying said feedback in one of the formulas w = - S -1 Φ -1 MD i ω v or w = - S -1 Φ -1 MX Δ X -1 M -1 Φ f, wherein w is a vector representing the linear load-dependent winch speed, S is a stiffness matrix, Φ is a coupling matrix, M is a mass matrix, D is a damping matrix, i is the imaginary unit, ω is the angular frequency, v is a speed vector, X is an eigenmatrix, Δ is a diagonal matrix representing decay factors, and f is a force vector, or tuning of standard PI-type winch speed controllers, where a boom winch speed controller is tuned to absorb vibration energy most efficiently around the lowest crane resonance frequency and where a hoist winch speed controller is tuned to absorb vibration energy most efficiently around the highest crane resonance frequency and - adding this damping motion to a motion set by a crane operator. - determining resonance frequencies of the coupled crane boom and load system, either experimentally or theoretically at least from data on inertia of the boom and stiffness of at least a boom rope, a hoist rope, a pedestal and an A-frame; - automatic generation of a damping motion in at least one of said winches (24, 36), that counteract dynamic oscillations in the crane by means of either: feedback of high-pass- or band-pass-filtered values of measured tension forces in the boom rope and in the hoist rope by applying said feedback in one of the formulas w = - S -1 Φ -1 MD i ω v or w = - S -1 Φ -1 MX Δ X -1 M -1 Φ f, wherein w is a vector representing the linear load-dependent winch speed, S is a stiffness matrix, Φ is a coupling matrix, M is a mass matrix, D is a damping matrix, i is the imaginary unit, ω is the angular frequency, v is a speed vector, X is an eigenmatrix, Δ is a diagonal matrix representing decay factors, and f is a force vector, or tuning of standard PI-type winch speed controllers, where a boom winch speed controller is tuned to absorb vibration energy most efficiently around the lowest crane resonance frequency and where a hoist winch speed controller is tuned to absorb vibration energy most efficiently around the highest crane resonance frequency and feedback of high-pass- or band-pass-filtered values of measured tension forces in the boom rope and in the hoist rope by applying said feedback in one of the formulas w = - S -1 Φ -1 MD i ω v or w = - S -1 Φ -1 MX Δ X -1 M -1 Φ f, wherein w is a vector representing the linear load-dependent winch speed, S is a stiffness matrix, Φ is a coupling matrix, M is a mass matrix, D is a damping matrix, i is the imaginary unit, ω is the angular frequency, v is a speed vector, X is an eigenmatrix, Δ is a diagonal matrix representing decay factors, and f is a force vector, or tuning of standard PI-type winch speed controllers, where a boom winch speed controller is tuned to absorb vibration energy most efficiently around the lowest crane resonance frequency and where a hoist winch speed controller is tuned to absorb vibration energy most efficiently around the highest crane resonance frequency and - adding this damping motion to a motion set by a crane operator.